{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 23 "Courier" 1 10 0 0 0 0 0 0 0 0 0 0 3 0 0 1 }{CSTYLE " Blue Emphasis" -1 256 "Times" 0 0 0 0 255 1 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "Green Emphasis" -1 257 "Times" 1 12 0 128 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Maroon Emphasis" -1 258 "Times" 1 12 128 0 128 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Purple Emphasis" -1 264 "Times" 1 12 102 0 230 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Red Emphasis " -1 265 "Times" 1 12 255 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Dark Red Emphasis" -1 266 "Times" 1 12 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 279 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 280 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 282 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 283 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 284 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "Grey Em phasis" -1 285 "Times" 1 12 96 52 84 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 286 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 287 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 288 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 289 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 290 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 128 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 3 0 3 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 128 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Maple O utput" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Time s" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 3 3 1 0 1 0 2 2 15 2 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 "T imes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 } } {SECT 0 {PARA 3 "" 0 "" {TEXT -1 67 "A procedure for illustrating area s under graphs and area functions " }}{PARA 0 "" 0 "" {TEXT -1 37 "by \+ Peter Stone, Nanaimo, B.C., Canada" }}{PARA 0 "" 0 "" {TEXT -1 19 "Ver sion: 24.4.2004" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 24 "load calculus proced ures" }}{PARA 0 "" 0 "" {TEXT -1 17 "The Maple m-file " }{TEXT 285 10 "calculus.m" }{TEXT -1 37 " contains the code for the procedure " } {TEXT 0 8 "areaplot" }{TEXT -1 25 " used in this worksheet. " }}{PARA 0 "" 0 "" {TEXT -1 122 "It can be read into a Maple session by a comma nd similar to the one that follows, where the file path gives its loca tion. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "read \"K:\\\\Maple /procdrs/calculus.m\";" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "; " }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 51 "load extra colours and util ity routines for colours" }}{PARA 0 "" 0 "" {TEXT -1 17 "The Maple m-f ile " }{TEXT 285 9 "colours.m" }{TEXT -1 85 " contains the code for pr ocedures which provide enhancement of Maple's colour system." }}{PARA 0 "" 0 "" {TEXT -1 14 "The procedure " }{TEXT 0 8 "areaplot" }{TEXT -1 55 " makes use of some of the colour enhancemet procedures." }} {PARA 0 "" 0 "" {TEXT -1 122 "It can be read into a Maple session by a command similar to the one that follows, where the file path gives it s location. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "read \"K:\\ \\Maple/procdrs/colours.m\";" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 43 "Graphs of antiderivatives as area functio ns" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "" {TEXT -1 226 "In each of the following examples the constant of integr ation is chosen so that the antiderivative has the value zero at the s tart of the plotting interval. This ensures that it gives the signed a rea between the graph and the " }{TEXT 267 1 "x" }{TEXT -1 33 " axis o ver the plotting interval." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Example 1" }}{PARA 0 "" 0 " " {TEXT -1 15 "The graphs of " }{XPPEDIT 18 0 "f(x) = 1/sqrt(x);" "6# /-%\"fG6#%\"xG*&\"\"\"F)-%%sqrtG6#F'!\"\"" }{TEXT -1 26 " and its ant iderivative " }{XPPEDIT 18 0 "g(x) = 2*sqrt(x)-2;" "6#/-%\"gG6#%\"xG, &*&\"\"#\"\"\"-%%sqrtG6#F'F+F+F*!\"\"" }{TEXT -1 17 " on the interval \+ " }{XPPEDIT 18 0 "[1,4]" "6#7$\"\"\"\"\"%" }{TEXT -1 1 "." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "f := x -> 1/sqrt(x);\nInt(f(t),t=1..x);\nvalue(%);\ng := unapply(%,x);\npl ot([f(x),g(x)],x=1..4,color=[red,blue]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*&\"\"\"F--%%sqrtG6#9$! \"\"F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*&\"\"\"F'*$-%% sqrtG6#%\"tGF'!\"\"/F,;F'%\"xG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$ -%%sqrtG6#%\"xG\"\"\"\"\"#F*!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"gGf*6#%\"xG6\"6$%)operatorG%&arrowGF(,&*$-%%sqrtG6#9$\"\"\"\"\"#F3! \"\"F(F(F(" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-% 'CURVESG6$7S7$$\"\"\"\"\"!F(7$$\"31++]i9Rl5!#<$\"3CtR^o7D)o*!#=7$$\"34 +]PC#)GA6F.$\"3=#\\F80u%R%*F17$$\"3%****\\Peui=\"F.$\"3ydZiRyO\"=*F17$ $\"33++D'3&o]7F.$\"3M5C'z(=#=%*)F17$$\"3/+](oX*y98F.$\"3/R')\\&f76s)F1 7$$\"3#***\\P9CAu8F.$\"3S!3v#\\5WI&)F17$$\"3.+]P*zhdV\"F.$\"3?N(z=yBcM )F17$$\"3++]P>fS*\\\"F.$\"3!H&)yB<$em\")F17$$\"35+](=$f%Gc\"F.$\"3us>U hX6**zF17$$\"3$*****\\#y,\"G;F.$\"3\\_'R$>#pr$yF17$$\"37++Dr\"zbo\"F.$ \"3\\H$z>`)Q-xF17$$\"3%*****\\(4&G] F.$\"3_DUf\\\"f$*=(F17$$\"3,++]siL-?F.$\"3)pS<8WTp1(F17$$\"3-+++!R5'f? F.$\"3Y$y&o0\"*)z'pF17$$\"3)***\\P/QBE@F.$\"3'e]5Ny_z&oF17$$\"3!****** \\\"o?&=#F.$\"3;5(*)=x!yknF17$$\"3%)**\\Pa&4*\\AF.$\"3#*H]Ak1!om'F17$$ \"3&)**\\7j=_6BF.$\"37$*G,x1NxlF17$$\"33++vVy!eP#F.$\"3S&>I9b`x['F17$$ \"3K+](=WU[V#F.$\"33NMG,2i3kF17$$\"3)****\\7B>&)\\#F.$\"3rV\\e$>HkK'F1 7$$\"3)***\\P>:mkDF.$\"3,$4F\"GuJWiF17$$\"3'***\\iv&QAi#F.$\"3Wnzo:IQv hF17$$\"31++vtLU%o#F.$\"3?%zFVRPM5'F17$$\"37+++bjm[FF.$\"3R$y2&Q'*oJgF 17$$\"3\"****\\(yb^6GF.$\"3-'zS9w\"*Q'fF17$$\"3)***\\PMaKsGF.$\"3^NOk= MU+fF17$$\"3=++D6W%)RHF.$\"3))H^4jFFKeF17$$\"3z*****\\@80+$F.$\"3m@\\) Q\"*3Ix&F17$$\"31++]7,HlIF.$\"3&3_`6Z%o6dF17$$\"3()**\\P4w)R7$F.$\"3E( e&e$yqxl&F17$$\"3;++]x%f\")=$F.$\"3HpYQ/5a+cF17$$\"3!)**\\P/-a[KF.$\"3 #p>Z'\\\"[#[bF17$$\"3/+](=Yb;J$F.$\"3Eh\"**o5B^\\&F17$$\"3')****\\i@Ot LF.$\"365,T*zJYW&F17$$\"3')**\\PfL'zV$F.$\"3q2W9?aB$R&F17$$\"3>+++!*>= +NF.$\"3cbzXve3X`F17$$\"3-++DE&4Qc$F.$\"3!Q.&pOf:(H&F17$$\"3=+]P%>5pi$ F.$\"3!3z5@-u3D&F17$$\"39+++bJ*[o$F.$\"3.U)*QL\")R4_F17$$\"33++Dr\"[8v $F.$\"3)3$\\I)y\\I;&F17$$\"3++++Ijy5QF.$\"3&f:%H/miA^F17$$\"31+]P/)fT( QF.$\"3OF\\\"[!fb!3&F17$$\"31+]i0j\"[$RF.$\"3\"f7$F3$\"3%zV'>W6i(=\"F17$F8$\"3w!*HTCmC$y\"F17$F=$ \"3w3JMLl!oO#F17$FB$\"3ycFc&y`G$HF17$FG$\"3)z\"o$))eYaW$F17$FL$\"33%)o &fjbY'RF17$FQ$\"37PiY*HY+\\%F17$FV$\"3U63%=InF+&F17$Fen$\"3uS?_^$=%>bF 17$Fjn$\"3!QWenNrf'fF17$F_o$\"3KZ^Sd\"o'fkF17$Fdo$\"3#RJP@g#HYpF17$Fio $\"3RHb`o822uF17$F^p$\"3]m?u-7*)=yF17$Fcp$\"3F[l;njy+$)F17$Fhp$\"30'\\ a*=bo-()F17$F]q$\"3wC`@u?Aj\"*F17$Fbq$\"373(G%*3!*[c*F17$Fgq$\"3_zp5Bq R****F17$F\\r$\"3=k5FyztS5F.7$Far$\"3_b4;b6t#3\"F.7$Ffr$\"3%ossaL'z?6F .7$F[s$\"37#oi5+T8;\"F.7$F`s$\"3dWg`C@\"H?\"F.7$Fes$\"3q'G*f7bmQ7F.7$F js$\"33l1J+?%oF\"F.7$F_t$\"3!>pLYZ?eJ\"F.7$Fdt$\"3M:RX>\\^`8F.7$Fit$\" 3m+/z^se*Q\"F.7$F^u$\"3%G;%\\(*[>H9F.7$Fcu$\"3]+\\G2zRk9F.7$Fhu$\"3yN$ Hq)Rf,:F.7$F]v$\"3&>0@\\;h\\`\"F.7$Fbv$\"3%4F^kd$3r:F.7$Fgv$\"3xBcfN9u /;F.7$F\\w$\"3\\Dw7!*3fR;F.7$Faw$\"3[q[F.7$Fiy$\"3 ?5G1%4xl$>F.7$F^z$\"3%R')G7Gus'>F.7$Fcz$\"\"#F*-Fhz6&FjzF^[lF^[lF[[l-% +AXESLABELSG6$Q\"x6\"Q!6\"-%%VIEWG6$;F(Fcz%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Example 2" }}{PARA 0 "" 0 "" {TEXT -1 16 " The graphs of " }{XPPEDIT 18 0 "f(x) = sin(x);" "6 #/-%\"fG6#%\"xG-%$sinG6#F'" }{TEXT -1 24 " and its antiderivative " } {XPPEDIT 18 0 "g(x) = 1-cos(x);" "6#/-%\"gG6#%\"xG,&\"\"\"F)-%$cosG6#F '!\"\"" }{TEXT -1 18 " on the interval [" }{XPPEDIT 18 0 "0,Pi;" "6$\" \"!%#PiG" }{TEXT -1 2 "]." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "f := x -> sin(x);\nInt(f(t),t=0..x );\nvalue(%);\ng := unapply(%,x);\nplot([f(x),g(x)],x=0..2*Pi,color=[r ed,blue]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG%$sinG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$-%$sinG6#%\"tG/F);\"\"!%\"xG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$cosG6#%\"xG!\"\"\"\"\"F)" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6#%\"xG6\"6$%)operatorG%&arrow GF(,&-%$cosG6#9$!\"\"\"\"\"F2F(F(F(" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$7en7$$\"\"!F)F(7$$\"3i]cC&eb&p8!#=$ \"3+9&o'z\"y_O\"F-7$$\"3YqR*pd)>hDF-$\"3K!y=V&*)GLDF-7$$\"3Zs[E^dK,RF- $\"3R]F<<.6.QF-7$$\"3ab^NehL]_F-$\"3I,*y(H4U7]F-7$$\"35*QhW&\\$Hf'F-$ \"3%=pD*eceDhF-7$$\"3zS11.fpPyF-$\"3w>82*oU&fqF-7$$\"3upr'fwtl7*F-$\"3 @)*QjP!>8\"zF-7$$\"3!QRa&4L&f/\"!#<$\"3[[%3w7ESl)F-7$$\"3YjXwg<#)y6FQ$ \"3Pi.Z,bcT#*F-7$$\"36qGW%H$\\:8FQ$\"3!e$pSF\"oen*F-7$$\"3SH22vMov8FQ$ \"35_*\\T'zD5)*F-7$$\"3$*)e)pbO(eV\"FQ$\"3#ffI'ft64**F-7$$\"3/]+3VNj.: FQ$\"3)\\\"3MzUXx**F-7$$\"396:YIMRr:FQ$\"2-6Ot@)******FQ7$$\"3Z'z]kaJ% R;FQ$\"3Ay8:y_Xw**F-7$$\"3!=3SCmpuq\"FQ$\"3s;Nd#HZn!**F-7$$\"33u?N%*p. tFQ$\"3cBCb^l'3E*F-7$$\"3#=uye<)G*4#FQ$\"3;2*>c4&oN')F-7$$\"3Ua[#o!GC >AFQ$\"3Se*Rp1I-(zF-7$$\"3-YwJf&y(eBFQ$\"3c:s(f4sF0(F-7$$\"3oNrpV8H#[# FQ$\"3(y]$4EukDhF-7$$\"3EzY)QW/yh#FQ$\"3?Pawd/k,]F-7$$\"35v)>8'\\%ou#F Q$\"3i\"*R%R(HvXQF-7$$\"3w$GCS?&[\")GFQ$\"3!\\o6f)Q%=d#F-7$$\"3Z%)='p( p70IFQ$\"3Kh5Xo]Ug8F-7$$\"3sA%)\\K8\\QJFQ$\"3^)pb)>hJ,J!#?7$$\"3c&fJlT >qF$FQ$!3)[9aqyJ,N\"F-7$$\"39l2\"4_3wR$FQ$!3w\"*=GeHGKDF-7$$\"3MOnGd![ y_$FQ$!39*)zsmMAnPF-7$$\"3#*=4JU#)RiOFQ$!3#35.)=3zv\\F-7$$\"3%G,f%[$HS z$FQ$!3!fgI[?W72'F-7$$\"3KoE+7#*Q@RFQ$!3#=$4p_xMJqF-7$$\"3y(f0ii+G1%FQ $!3WWqZN&GL'zF-7$$\"3;fORr]')*=%FQ$!33*3&3nLil')F-7$$\"3R&p%*z[LbK%FQ$ !3]$[$Q0***4E*F-7$$\"3M'pExBp%[WFQ$!3'R4g7n[Pl*F-7$$\"3,z&[2')pc^%FQ$! 30-Py@682)*F-7$$\"3oh/x$[qGe%FQ$!3$euj/)>C;**F-7$$\"3qQq'H.,hk%FQ$!3Ie f(ReP!y**F-7$$\"3e;O;#eJ$4ZFQ$!3;'*phhK&*****F-7$$\"3sU'G^sDax%FQ$!311 %\\AUQ,)**F-7$$\"3&)oO4o)>:%[FQ$!32^6Oe=u;**F-7$$\"3;@9vt*Qh!\\FQ$!31K )*)[7\"*G\")*F-7$$\"3Ou\"4%z!e2(\\FQ$!3_#49llz!o'*F-7$$\"3*zX#[4&eg5&F Q$!3]_&yQBx]B*F-7$$\"3n*e![/*ojB&FQ$!3o\"*oMmwMe')F-7$$\"3#ob8X5I'p`FQ $!3Froqht!o\"zF-7$$\"3PA\"GX$yy,bFQ$!3x5TwV@sUqF-7$$\"39L1/jqABcFQ$!3) \\'4LY'Q38'F-7$$\"3mweKB,TidFQ$!3iCF-zq_v\\F-7$$\"3'oIe;6(*o)eFQ$!3s)y _Bpo*fQF-7$$\"3nKcu0ii>gFQ$!3dChVjR=0EF-7$$\"3w)*zj%)[mYhFQ$!3]'*=#eVn 4O\"F-7$$\"3)****>YH&=$G'FQ$!3/UE[]'efD\"!#D-%'COLOURG6&%$RGBG$\"*++++ \"!\")F(F(-F$6$7enF'7$$\"3;`#Gi#zxZo!#>$\"3S?CdvqoVBFbt7$F+$\"3C3I2kDw j$*Fbt7$$\"3q5)>63x`'>F-$\"3T_-F]^l7$F1$\"3;v@&z**y>E$F]^l7$F6$ \"3P!*Rzz^89vF]^l7$F;$\"3!\\(*)fv!HpM\"F-7$F@$\"3sh[_ezu&4#F-7$FE$\"3 \"y/y&>eUtmp8YZ(F-7$F^o$\"3'\\$f3ZJ'[l)F-7$Fho$\"3TL6j.rf+5FQ7$ Fbp$\"3+7?KK#[i8\"FQ7$F\\q$\"3u()*f7@=YE\"FQ7$Faq$\"3W#pX#*)3Jx8FQ7$Ff q$\"31O<]B:B/:FQ7$F[r$\"37&)*oQ%*[Rg\"FQ7$F`r$\"3'\\\"Q8J;$*3r1$f'=FQ7$F_s$\"3I:T1DO4B>FQ7$Fds$\"3%3Gi $\\BOm>FQ7$$\"3*Q3$\\!41L%HFQ$\"3_#)eOYbS!)>FQ7$Fis$\"3a262,Iq!*>FQ7$$ \"3g`,ta\"4=2$FQ$\"3w$R!e>hc(*>FQ7$F^t$\"3!))f24>&****>FQ7$$\"3#*3]^u` v2KFQ$\"372K]X?\"y*>FQ7$Fdt$\"3qzW\"G!Q%3*>FQ7$$\"3e!=@(oRJPLFQ$\"3OI2 hZw!4)>FQ7$Fit$\"3_3vb[lSn>FQ7$F^u$\"3n_M8CiKE>FQ7$Fcu$\"3Is/4<'=u'=FQ 7$Fhu$\"3!)oJ.#y1Yz\"FQ7$F]v$\"3m42e*fc5r\"FQ7$Fbv$\"3Y@9!*\\'e[g\"FQ7 $Fgv$\"3OTrb\\)o!*\\\"FQ7$F\\w$\"3]YDqc\"ysP\"FQ7$Faw$\"3_GUFnl'3E\"FQ 7$F[x$\"3\"3d,soc\"H6FQ7$Fex$\"3?5yX$RdI+\"FQ7$F_y$\"3f5#4'[oF7()F-7$F iy$\"3^wXjc(e\\W(F-7$F^z$\"3/L!e[r,U;'F-7$Fcz$\"35$**\\/_*p'*\\F-7$Fhz $\"3%z>P5p\\1*QF-7$F][l$\"3sj]/'p*p+HF-7$Fb[l$\"3m@Epz;#)*4#F-7$Fg[l$ \"3w:Y%[aicK\"F-7$F\\\\l$\"3qW9t^4**\\xF]^l7$Fa\\l$\"3O0MsT;6`MF]^l7$$ \"3G:=>Xb9$3'FQ$\"33535UA8%*>F]^l7$Ff\\l$\"3YL/&[=[WI*Fbt7$$\"3P***G'* 3D\\@'FQ$\"3z)o$e%=C)GBFbt7$F[]l$\"3ac^iCIA56!#L-Fa]l6&Fc]lF(F(Fd]l-%+ AXESLABELSG6$Q\"x6\"Q!6\"-%%VIEWG6$;F($\"+3`=$G'!\"*%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Example 3" }}{PARA 0 "" 0 "" {TEXT -1 16 " The graphs of " }{XPPEDIT 18 0 "f(x) = (1-x^2 )/((1+x^2)^2);" "6#/-%\"fG6#%\"xG*&,&\"\"\"F**$F'\"\"#!\"\"F**$,&F*F** $F'F,F*F,F-" }{TEXT -1 26 " and its antiderivative " }{XPPEDIT 18 0 "g(x) = x/(1+x^2);" "6#/-%\"gG6#%\"xG*&F'\"\"\",&F)F)*$F'\"\"#F)!\"\" " }{TEXT -1 18 " on the interval " }{XPPEDIT 18 0 "[0,4]" "6#7$\"\"! \"\"%" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 131 "with(plots):\nf := x -> (1-x^2)/(1+x^2)^ 2;\nInt(f(t),t=0..x);\nvalue(%);\ng := unapply(%,x);\nplot([f(x),g(x)] ,x=0..4,color=[red,blue]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf* 6#%\"xG6\"6$%)operatorG%&arrowGF(*&,&\"\"\"F.*$)9$\"\"#F.!\"\"F.*$),&F .F.F/F.F2F.F3F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*&,&\" \"\"F(*$)%\"tG\"\"#F(!\"\"F(*$),&F(F(F)F(F,F(F-/F+;\"\"!%\"xG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"xG\"\"\",&F%F%*$)F$\"\"#F%F%!\"\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6#%\"xG6\"6$%)operatorG%&a rrowGF(*&9$\"\"\",&F.F.*$)F-\"\"#F.F.!\"\"F(F(F(" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$7in7$$\"\"!F)$\"\"\"F )7$$\"3ILLL3x&)*3\"!#>$\"3/2=$eLPk***!#=7$$\"3emmm;arz@F/$\"3?J9O,yv&) **F27$$\"3')*****\\7t&pKF/$\"35B=bGn)z'**F27$$\"39LLLL3VfVF/$\"3d-_B(> mJ%**F27$$\"3s******\\i9RlF/$\"3E3UD$[FE()*F27$$\"3Hmmmm;')=()F/$\"3kx 8b5L![x*F27$$\"3-++]7z>^7F2$\"3l`8Pj(>%F2$\"39Km'G\"R JbfF27$$\"3Q*****\\Z7Mf%F2$\"3/e;mE!o,Q&F27$$\"3Qmmm\">K'*)\\F2$\"3@P. 8MOg9[F27$$\"3IKLLeZ*)*R&F2$\"3-u6.1$elC%F27$$\"3P*****\\Kd,\"eF2$\"3# HD8R2)\\-PF27$$\"39KLLe9XMiF2$\"3_cr,:))**pJF27$$\"3-mmm\"fX(emF2$\"3) 4i522%orEF27$$\"3.*****\\U7Y](F2$\"3qla)3O\"e(y\"F27$$\"3'QLLLV!pu$)F2 $\"3vB\"=z:J<.\"F27$$\"3xmmm;c0T\"*F2$\"3e@-_#3`&z[F/7$$\"3#*******H,Q +5!#<$!31UX^Llc**=!#@7$$\"3)*******\\*3q3\"F^s$!3sEq,[?U:QF/7$$\"3)*** ****p=\\q6F^s$!3I]rpW0*ye'F/7$$\"3mmm;fBIY7F^s$!3Q3<&p!)*y'[)F/7$$\"3G LLLj$[kL\"F^s$!3F2m]@^q75F27$$\"3?LLL`Q\"GT\"F^s$!3mf2nP(R'46F27$$\"3! *****\\s]k,:F^s$!3?D%RXz/X=\"F27$$\"39LLL`dF!e\"F^s$!3?%p$Qc.X(\\7F27$$ \"3QLLLe/TM=F^s$!3&z5LC(pDT7F27$$\"3JLL$eDBJ\">F^s$!3z'**fA@B\\A\"F27$ $\"3immmTc-)*>F^s$!3\"y+f6[I1?\"F27$$\"3Mmm;f`@'3#F^s$!3yhr[ob?q6F27$$ \"3y****\\nZ)H;#F^s$!323IIARyS6F27$$\"3YmmmJy*eC#F^s$!338[]p>.26F27$$ \"3')******R^bJBF^s$!3gJgNhB\"42\"F27$$\"3f*****\\5a`T#F^s$!3MDVn!pW]. \"F27$$\"3o****\\7RV'\\#F^s$!32s9GY>L+5F27$$\"3k*****\\@fke#F^s$!3@aX, cy0A'*F/7$$\"3/LLL`4NnEF^s$!3))ywVFe)fG*F/7$$\"3#*******\\,s`FF^s$!3Q] )p]=pg$*)F/7$$\"3[mm;zM)>$GF^s$!3,cpGZp=G')F/7$$\"3$*******pfaZ/>'F/7$$\"3ILLLGUYoOF^s$!3M**o`]3$*ffF/7$$\"3_mmm1^rZ PF^s$!3#*45!o]FIw&F/7$$\"34++]sI@KQF^s$!3'R9PL!RJibF/7$$\"34++]2%)38RF ^s$!3+$fk9EK(y`F/7$$\"\"%F)$!3%37&o=9J!>&F/-%'COLOURG6&%$RGBG$\"*++++ \"!\")F(F(-F$6$7fn7$F(F(7$F>$\"3U*[g&3;;^VF/7$FH$\"3i#y8;>#3`')F/7$FM$ \"3d.a%4P7>B\"F27$FR$\"3=`JnVTG)e\"F27$FW$\"3c;*43srN(>F27$Ffn$\"3()G& e0Bc$RBF27$F[o$\"35b&*z\"*)*>&o#F27$F`o$\"3o\")R()o4d1IF27$Feo$\"3H5dI V9u+LF27$Fjo$\"3Eg*pj)HaoNF27$F_p$\"3e!)o)H[\"4$z$F27$Fdp$\"3_1(4E)e,& *RF27$F^q$\"3S&Gi$y`yVVF27$Fhq$\"3$f!ot/>F8YF27$F]r$\"3n#[et_D3![F27$F br$\"3h&[@e\"oOA\\F27$$\"3K+++DI(yv)F2$\"3YK&QE#>Mc\\F27$Fgr$\"3#4FPXI .*z\\F27$$\"3+LLLe%GCd*F2$\"3A7&4=(*H_*\\F27$F\\s$\"3M_-*)Q'*****\\F27 $$\"3&*******RXpV5F^s$\"3__DT%F27$F[v$\"3ke%fqE'z(*QF27$Fdw$\"3.p)\\(4c24QF27$ Fiw$\"3&>)=(o$z(er$F27$F^x$\"3B>YoqKfAOF27$Fcx$\"3#z*oN9JNMNF27$Fhx$\" 3Y*)**3@/%=X$F27$F]y$\"3eqQXWg]jLF27$Fby$\"3![qj!4d.(G$F27$Fgy$\"3[?Cy ; " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Example 4" }}{PARA 0 "" 0 "" {TEXT -1 17 " The graphs of " }{XPPEDIT 18 0 "f(x) = abs(x^2-4)-2;" "6#/-%\"fG6#%\"xG,&-%$absG6#,&*$F'\"\"#\"\"\"\"\"%! \"\"F/F.F1" }{TEXT -1 40 " and its antiderivative on the interval " } {XPPEDIT 18 0 "[-3,3]" "6#7$,$\"\"$!\"\"F%" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "f : = x -> abs(x^2-4)-2;\nInt(f(t),t=-3..x);\nvalue(%);\ng := unapply(%,x) ;\nplot([f(x),g(x)],x=-3..3,color=[red,blue]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(,&-%$absG6#,&* $)9$\"\"#\"\"\"F5\"\"%!\"\"F5F4F7F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$,&-%$absG6#,&*$)%\"tG\"\"#\"\"\"F/\"\"%!\"\"F/F.F1/F-;! \"$%\"xG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(-%*PIECEWISEG6%7$,&%\"xG !\"%*&#\"\"\"\"\"$F-)F)F.F-F-1F)!\"#7$,(F)\"\"%*&#F-F.F-*$F/F-F-!\"\"# \"#KF.F-1F)\"\"#7$,(F)F**&F,F-F/F-F-#\"#kF.F-2F%\"gGf*6#%\"xG6\"6$%)operatorG%& arrowGF(,(-%*piecewiseG6(19$!\"#,&F1!\"%*&#\"\"\"\"\"$F7)F1F8F7F71F1\" \"#,(F1\"\"%*&#F7F8F7*$F9F7F7!\"\"#\"#KF8F72F;F1,(F1F4*&F6F7F9F7F7#\"# kF8F7F7*&F;F7F1F7FA\"\"*FAF(F(F(" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$7_o7$$!\"$\"\"!$\"\"$F*7$$!3&***** \\P&3Y$H!#<$\"3N*)yOos#>h#F07$$!3!******\\2<#pGF0$\"3]a:ZBmSKAF07$$!3' )**\\78.K7GF0$\"3:(\\:OaX\"4>F07$$!3#)***\\7bBav#F0$\"3CgJyY*eBf\"F07$ $!3'***\\(=>P9p#F0$\"3,&)z!y:MQC\"F07$$!36++]K3XFEF0$\"36S%\\?xy\\.*!# =7$$!3w******H./jDF0$\"3%\\2l?Ld7$$!3#****\\i3@/P#F0$!3Y.Ph Q(Q5\"QFL7$$!3/++vG\"))4J#F0$!3=Ndw(oQLf'FL7$$!3;++Dr^b^AF0$!3'o#Q<3J* \\I*FL7$$!3/++D'y:+>#F0$!3?%zvf&3$Q?\"F07$$!3$****\\7Sw%G@F0$!3a\\=K4# )ep9F07$$!3=++D\"GK[1#F0$!3s>zI]wYOF07$$!3!****\\([\"[x$>F0$!3e^S)z)y'[v\"F07$$!3/++DO\"3V(=F0$!3d[Hh*)4 .8:F07$$!3#******\\V'zViUC\"F0$\"3B?y$4!f6=XFL7$$!3-++DhkaI6F0$\"3-B 5b*)pk=sFL7$$!3s******\\XF`**FL$\"3#HABtDB$45F07$$!3u*******>#z2))FL$ \"3S\">;c'zAC7F07$$!3S++]7RKvuFL$\"3uc?.C`>T9F07$$!3s,+++P'eH'FL$\"3oA -r-5i.;F07$$!3q)***\\7*3=+&FL$\"3ib$Gg2>)\\F07$$!32)***\\i6:.8FL$\"3+ \\nZqz,$)>F07$$!3Wb+++v`hH!#?$\"3)ej&HH7****>F07$$\"3]****\\(QIKH\"FL$ \"3#fY[;bvK)>F07$$\"38****\\7:xWCFL$\"3]%o;D#4BS>F07$$\"3E,++vuY)o$FL$ \"3Er'eo2_R'=F07$$\"3!z******4FL(\\FL$\"3IcScv,m_:F07$$\"30+]P\\`9Q>F0$!3'4%RI&R2kv\"F07 $$\"3P+++!)RO+?F0$!3Ye&=v%Ra)*>F07$$\"3A++D;:*R1#F0$!3@D![3-R*Rw7#F0$!3O-!Ru;PKZ\"F07$$\"3=+]i?(>2>#F0$!3?@Zm0ru+7F07$$\"3O ++v)Q?QD#F0$!3;rza_l$H?*FL7$$\"3K+]P\\L!=J#F0$!3/)H&=QFlblFL7$$\"3G+++ 5jypBF0$!3JHeO\\%G6%QFL7$$\"3B++DE8COCF0$!3_$)R;F+#GZ'Ffn7$$\"3<++]Ujp -DF0$\"35z(Gw#)*)[j#FL7$$\"33++D,X8iDF0$\"3ske&\\-K`k&FL7$$\"3++++gEd@ EF0$\"3#yv%f;@VE()FL7$$\"31+]PMh%\\o#F0$\"3)fD&\\Wd$*37F07$$\"39++v3'> $[FF0$\"3[`(R=ngKb\"F07$$\"39+++5h(*3GF0$\"31L2b'yY.*=F07$$\"37++D6Ejp GF0$\"3G%\\\\NK\"zMAF07$$\"31+]i0j\"[$HF0$\"3KtBwZn98EF07$F+F+-%'COLOU RG6&%$RGBG$\"*++++\"!\")$F*F*Fh`l-F$6$7bo7$F(Fh`l7$F4$\"3(GRu>**=yT$FL 7$F>$\"3s.,I.4`\"f&FL7$FC$\"39P-!*>=$oqN$FL7$F`q$\"3RekwIe%)G6FL7$Feq$!3y5V&4+-*R`Ffn7$Fjq$! 3jo%=kG(40:FL7$$!3%****\\7tNTc\"F0$!3K'Rz,u8/'=FL7$F_r$!3m1ihWRv%3#FL7 $$!3'********=eWV\"F0$!3c%GW\\U!p$=#FL7$Fdr$!3mc6bH5_h@FL7$$!3(****** \\QuoI\"F0$!3jM9Un^pI?FL7$Fir$!3SJ%)QpGS(z\"FL7$$!3'***\\7GVS(=\"F0$!3 hwX[?/!4]\"FL7$F^s$!3XHm,`ZiF6FL7$Fcs$\"3Y7]0sOM%p%F]v7$Fhs$\"3`2YZC_p G8FL7$F]t$\"3X()*f0;M%3JFL7$Fbt$\"3jcj#ok)y1\\FL7$Fgt$\"3[!G'3+z;!3(FL 7$F\\u$\"3:'Qfy#y31$*FL7$Fau$\"3/')otXg+v6F07$Ffu$\"3cEQ)e5unS\"F07$F[ v$\"3IA\\K+Oug;F07$Fav$\"3!*>f+#z\"fC>F07$Ffv$\"3Y7!oXC]2:#F07$F[w$\"3 #H1:q@LwQ#F07$F`w$\"3`Zug\"pG.i#F07$Few$\"3EpeEKa6KGF07$Fjw$\"3xR&4;)3 L=IF07$F_x$\"3s7x)*oy7*>$F07$Fdx$\"3A>VT4(eVL$F07$Fix$\"3c*R0-=?hW$F07 $$\"3!***\\(=sx#*=\"F0$\"3)3WA6kCX[$F07$F^y$\"3\"4E'HOSt9NF07$$\"3/+]( o3Z@J\"F0$\"3I%)ze:l!z`$F07$Fcy$\"3')pMEw?F]NF07$$\"3(***\\(=o*pO9F0$ \"3WD&Ru*ec^NF07$Fhy$\"3,5^v'y$QUNF07$$\"3%)***\\im&>g:F0$\"3UHJ0m(46_ $F07$F]z$\"3/l())\\b0u[$F07$$\"3!***\\PCw,&o\"F0$\"37&\\gO$Q&>W$F07$Fb z$\"3'o9b@(*pOQ$F07$Fgz$\"3hy:.t[*z@$F07$Fa[l$\"3/]*y\\Is#**HF07$F[\\l $\"37\")=!z'z-yFF07$Fe\\l$\"3M@)\\qdfmi#F07$Fj\\l$\"3]cu\"RgS4e#F07$F_ ]l$\"3!RP\">1jw]DF07$$\"3E+]7=Q,.CF0$\"3([_Zb#=jSDF07$Fd]l$\"3#*z9%G_. e`#F07$$\"3?+]PM)o%pCF0$\"35UL))oZNODF07$Fi]l$\"3DKK[M*eBa#F07$F^^l$\" 3'y-0M*>$pc#F07$Fc^l$\"3S@q?b&3'4EF07$Fh^l$\"3KJMY!eCbn#F07$F]_l$\"3U' z0B:2Iw#F07$Fg_l$\"3M!RladzC*HF07$F+$\"3:KLLLLLLLF0-Fb`l6&Fd`lFh`lFh`l Fe`l-%+AXESLABELSG6$Q\"x6\"Q!6\"-%%VIEWG6$;F(F+%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Example 5" }}{PARA 0 "" 0 "" {TEXT -1 16 " The graph of " }{XPPEDIT 18 0 "f(x) = PIECEWISE([ -1, x < 0],[1, 0 < x]);" "6#/-%\"fG6#%\"xG-%*PIECEWISEG6$7$,$\"\"\"!\" \"2F'\"\"!7$F-2F0F'" }{TEXT -1 26 " and its antiderivative " } {XPPEDIT 18 0 "g(x) = abs(x)-1.5;" "6#/-%\"gG6#%\"xG,&-%$absG6#F'\"\" \"-%&FloatG6$\"#:!\"\"F1" }{TEXT -1 17 " on the interval " }{XPPEDIT 18 0 "[-1.5, 1.5]" "6#7$,$-%&FloatG6$\"#:!\"\"F)-F&6$F(F)" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 118 "f := x -> piecewise(x<0,-1,x>=0,1):\ng := x -> abs(x )-1.5:\nplot([f(x),g(x)],x=-1.5..1.5,color=[red,blue],discont=true);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6%7S 7$$!3++++++++:!#<$!\"\"\"\"!7$$!3W\"R:)oUIn9F*F+7$$!38)yMz)e&)Q9F*F+7$ $!3eu7J3F'oS\"F*F+7$$!35&oDrXdYP\"F*F+7$$!3R*Gx=F0EM\"F*F+7$$!3OAn=$z) )GJ\"F*F+7$$!3uh#[25>@G\"F*F+7$$!3'e!>\"3/(H]7F*F+7$$!3%fMDY.x&=7F*F+7 $$!3#=5y$4\"\\f=\"F*F+7$$!3Kz01:/@d6F*F+7$$!3?&G+?Xd[7\"F*F+7$$!3qc_cW ;P#4\"F*F+7$$!3#*oyi\\b1h5F*F+7$$!3pEsC;mjK5F*F+7$$!3=jL_Z'=$))**!#=F+ 7$$!3$R5'fg![>q*FhnF+7$$!3%*QtQ*)4$)o$*FhnF+7$$!3mo?&o$f'R2*FhnF+7$$!3 )e4C1C_/v)FhnF+7$$!3`=-\\(p!RU%)FhnF+7$$!3my!3]zg47)FhnF+7$$!3>CM(\\!y yDyFhnF+7$$!3B$>N(eQS2vFhnF+7$$!3C:;x=CpwrFhnF+7$$!3'eQ(4Qr!)))oFhnF+7 $$!3[LU4[J)yd'FhnF+7$$!3'[m'[U#omD'FhnF+7$$!3\\c^OC@UUfFhnF+7$$!3Cb#[o %GPQcFhnF+7$$!3HX%[J'zx+`FhnF+7$$!3;M^+XRV(*\\FhnF+7$$!3M,H:e%\\Nn%Fhn F+7$$!3?x[Ou>1!Q%FhnF+7$$!3Y$f\"QME?fSFhnF+7$$!3Y./h+!*HdPFhnF+7$$!39b :u8FsTMFhnF+7$$!3PAOB6#*=LJFhnF+7$$!3cMY]FK=5GFhnF+7$$!3o>=+v+4*\\#Fhn F+7$$!3'f4)Q%R_4=#FhnF+7$$!3e,TRa!\\a'=FhnF+7$$!3EJ*[=DMbd\"FhnF+7$$!3 =#[j7F+7$$!3Mwfmo+,#H'F`tF+7$$!3qN;B7]= fKF`tF+7$$!3)***************H!#EF+7S7$$\"3)***************HFjt$\"\"\"F -7$$\"3S`3Y=MdpKF`tF_u7$$\"3Cx6_1:T9hF`tF_u7$$\"3bSD()o%HPJ*F`tF_u7$$ \"3E\\JueaU`7FhnF_u7$$\"3=0rA6t%Rd\"FhnF_u7$$\"3cvF8)476(=FhnF_u7$$\"3 u\"Q0)H&FhnF_u7$$\"3LhEhS!p6j&FhnF_u7$$\"3hJz9$4Mg #fFhnF_u7$$\"3Q/fP*yZ&\\iFhnF_u7$$\"3u\"y4DL4wb'FhnF_u7$$\"3g@>*\\BR!z oFhnF_u7$$\"33wl-DA@urFhnF_u7$$\"3/2[Erhf#\\(FhnF_u7$$\"3.&QG7h2L#yFhn F_u7$$\"3R9E!>*G>6\")FhnF_u7$$\"3zmd!>)o6A%)FhnF_u7$$\"3SNL^(yJLu)FhnF _u7$$\"3yV[j0zdd!*FhnF_u7$$\"3-X<:$=F;O*FhnF_u7$$\"3'\\b^o1A#*p*FhnF_u 7$$\"3h'[*\\3mD+5F*F_u7$$\"3*)4Z=d]kK5F*F_u7$$\"3I7Nc0Q*>1\"F*F_u7$$\" 3oS=cR(zS4\"F*F_u7$$\"3of*QH5qU7\"F*F_u7$$\"3_WeiJx#e:\"F*F_u7$$\"3yPm (=3\"o'=\"F*F_u7$$\"3dO&\\-o\")*=7F*F_u7$$\"31=)*\\&*44]7F*F_u7$$\"3W! >hNw/>G\"F*F_u7$$\"3()*egv4bMJ\"F*F_u7$$\"3!p5:ydYCM\"F*F_u7$$\"3!=lte 3ucP\"F*F_u7$$\"3`8#*=lJR09F*F_u7$$\"3ESLJ-*zqV\"F*F_u7$$\"3o$oxG:3uY \"F*F_u7$$\"3++++++++:F*F_u-%'COLOURG6&%$RGBG$\"*++++\"!\")$F-F-Fh^l-F $6$7U7$F(Fh^l7$$!3&*****\\P&3YV\"F*$!3F0++]i9RlF`t7$$!3!***\\ivfS*\\Fhn7$$!3;++D\"oS:P*Fhn$!3$)***\\(=$f%GcFhn7$$ !3h*****\\<#)*=()Fhn$!3Q+++Dy,\"G'Fhn7$$!3#*****\\(G3U9)Fhn$!33++]7mPPFhn$!3)***\\P/QBE6F*7$$!3'3+++&=$z9$F hn$!3!******\\\"o?&=\"F*7$$!3N***\\iX/4]#Fhn$!31+]Pa&4*\\7F*7$$!3C*** \\(o8y%)=Fhn$!33+]7j=_68F*7$$!33****\\i:#>C\"Fhn$!33++vVy!eP\"F*7$$!3O !***\\7ev:lF`t$!34+](=WU[V\"F*7$$!3d'**\\PM;>L$F`t$!3#**\\il$3om9F*7$$ !3uF++](o2[\"!#?$!3)****\\7B>&)\\\"F*7$$\"3U(**\\7`P!fJF`t$!3/+voC'4%o 9F*7$$\"3i(***\\P>:mkF`t$!3-+]i![Q`V\"F*7$$\"3d***\\iv&QA7Fhn$!3/+]PC9 wx8F*7$$\"3j++]PPBW=Fhn$!3%****\\iiwbJ\"F*7$$\"3%*)*****\\Nm'[#Fhn$!35 +++XOL^7F*7$$\"36****\\(yb^6$Fhn$!33++D@W[)=\"F*7$$\"3')***\\PMaKs$Fhn $!3-+]ilXnF6F*7$$\"3a****\\7TW)R%Fhn$!3/++v)eb,1\"F*7$$\"3*y*****\\@80 ]Fhn$!35-++]y'[***Fhn7$$\"3_+++D6!Hl&Fhn$!3[*****\\())4Z$*Fhn7$$\"3j)* *\\P4w)RiFhn$!3Q,+D1R7g()Fhn7$$\"3s,++vZf\")oFhn$!3G)****\\A0%=\")Fhn7 $$\"3'z**\\P/-a[(Fhn$!3/-+Dczf9vFhn7$$\"3R++v=Yb;\")Fhn$!3g***\\7QXM)o Fhn7$$\"3s)****\\i@Ot)Fhn$!3G,++v$yjE'Fhn7$$\"3g)**\\PfL'z$*Fhn$!3R,+D 1kO?cFhn7$$\"3>+++!*>=+5F*$!37)******4!=)*\\Fhn7$$\"3-++DE&4Q1\"F*$!3u ****\\PZ!>O%Fhn7$$\"3=+]P%>5p7\"F*$!3E)**\\i0)*3t$Fhn7$$\"39+++bJ*[=\" F*$!3e)*****\\%o5:$Fhn7$$\"33++Dr\"[8D\"F*$!39****\\(G=l[#Fhn7$$\"3+++ +Ijy58F*$!3+++++n8#*=Fhn7$$\"31+]P/)fTP\"F*$!3G***\\i&>Se7Fhn7$$\"31+] i0j\"[V\"F*$!3V$***\\P%p$=lF`t7$F_^lFh^l-Fb^l6&Fd^lFh^lFh^lFe^l-%+AXES LABELSG6%Q\"x6\"Q!6\"%(DEFAULTG-%%VIEWG6$;$!#:F,$\"#:F,F]_m" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }} }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 41 "A procedure for plotting area functions: \+ " }{TEXT 0 8 "areaplot" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 15 "" 0 "" {TEXT -1 14 " The procedure " }{TEXT 0 8 "areaplot" }{TEXT -1 197 " plots the graph \+ of a function and shows the regions between the graph and the horizont al axis as shaded regions with different colours depending on whether \+ the graph is above or below the x axis. " }}{PARA 15 "" 0 "" {TEXT -1 106 "The procedure can also be used to give an animated construction o f the antiderivative of a given function." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 16 "areaplot: usage " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 259 18 "Calling Sequen ce:\n" }}{PARA 0 "" 0 "" {TEXT 260 4 " " }{TEXT -1 21 "areaplot( fx , xrng )\n" }{TEXT 262 1 "\n" }{TEXT -1 32 " areaplot( fx, xrng, yr ng ) \n" }}{PARA 256 "" 0 "" {TEXT -1 11 "Parameters:" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 163 " fx - an expr ession involving a single variable, say x.\n\n xrng - an eq uation of the form x=a..b, where a..b is the range for the area to be \+ shown." }}{PARA 0 "" 0 "" {TEXT -1 62 " and also \+ the horizontal plotting range.\n" }}{PARA 0 "" 0 "" {TEXT -1 11 " \+ " }{TEXT 264 2 "OR" }{TEXT -1 103 ": an equation of the form \+ x=[a..b,c..d], where the range a..b is the range for the area to be sh own " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 66 " and c..d is the horizontal plotting range." }} {PARA 0 "" 0 "" {TEXT -1 12 " " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 4 " " }{TEXT 23 7 "yrng - " } {TEXT -1 92 " vertical range (optional), which can be given in the form s..t, or in the form y=s..t.\n" }}{PARA 0 "" 0 "" {TEXT -1 5 " \+ " }}{PARA 256 "" 0 "" {TEXT -1 12 "Description:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT -1 14 "The procedure " }{TEXT 0 8 "areaplot" }{TEXT -1 196 " plots the graph of a function and shows the regions between the graph and the horizontal axis as shaded regio ns with different colours depending on whether the graph is above or b elow the x axis." }}{PARA 15 "" 0 "" {TEXT -1 104 "Zeros of the functi on can be displayed if desired. (Only zeros in which a sign change occ urs are given.)" }}{PARA 15 "" 0 "" {TEXT -1 141 "The signed areas of \+ any separate regions cut off above and below the horizontal axis by th e graph over the specified range can be displayed.." }}{PARA 15 "" 0 " " {TEXT -1 88 "An animation in which the area involved is swept out fr om left to right can be produced." }}{PARA 15 "" 0 "" {TEXT -1 73 "The area function can be plotted in conjunction with the area animation. \n" }}{PARA 0 "" 0 "" {TEXT 261 8 "Options:" }{TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT -1 186 "color=[colour1,colour2] or color=colour1 \ncol our1 is the colour for the segments of the graph above the horizontal \+ axis, colour2 is the colour for the segments below the horizontal axis ." }}{PARA 0 "" 0 "" {TEXT -1 74 "If a single color is given, the whol e graph is coloured with that colour. " }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 66 "shading=[colour1,colour2] or shading= colour1 or shading=lighten[t]" }}{PARA 0 "" 0 "" {TEXT -1 143 "colour1 is the colour for the regions above the horizontal axis, colour2 is t he colour for the regions below and colour3 is for the area graph." }} {PARA 0 "" 0 "" {TEXT -1 113 "If a single color is given, all regions \+ between the graph and the horizontal axis are coloured with that colou r. " }}{PARA 0 "" 0 "" {TEXT -1 362 "If shading=lighten[t], then the r egions between the graph and the horizontal axis are coloured by light ening the colour or colours specified for the corresponding segments o f the graph. The extent of the lightening can be specified by the subs cript parameter t, where t is between 0 and 1, the default value being \"shading=light[.8]\" if the subscript is omitted." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "ord_colour=colour1 or o rd_color=color1" }}{PARA 0 "" 0 "" {TEXT -1 115 "This option controls \+ the colour of the ordinate lines which give the left and right boundar y lines for the region. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 11 "ord_style=n" }}{PARA 0 "" 0 "" {TEXT -1 67 "This o ption controls the linestyle of the ordinate boundary lines. " }} {PARA 0 "" 0 "" {TEXT -1 17 "\nzeros=true/false" }}{PARA 0 "" 0 "" {TEXT -1 227 "If \"zeros\" is true, then the zeros are displayed.\n\na reas=true/false\nIf \"areas\" is true, then the numerical values of th e signed areas of individual regions cut off by the graph above and be low the horizontal axis are displayed." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 20 "animation=true/false" }}{PARA 0 "" 0 "" {TEXT -1 79 "If \"animation\" is true, then the frames for the area animation are constructed." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 23 "areafunction=true/false" }}{PARA 0 "" 0 "" {TEXT -1 121 "If \"areafunction\" is true, then frames including both \+ the area function animation and the area animation are constructed." } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 85 "frames=n \nThe number of frames for the animation. The default value of \"frame s\" is 30." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 142 "numerical=true/false\nThe area function can be constructed usi ng numerical integration if a closed formula for the integral cannot b e obtained." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 263 31 "Available standard plot options" }{TEXT -1 42 ": scaling, num points, xtickmarks, labels." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 264 16 "How to activat e:" }{TEXT 256 1 "\n" }{TEXT -1 155 "To make the procedures active ope n the subsection, place the cursor anywhere after the prompt [ > and \+ press [Enter].\nYou can then close up the subsection." }}{PARA 0 "" 0 "" {TEXT 264 4 "Note" }{TEXT -1 95 ": The utilty routines for the enha nced colour system must be loaded in order for the procedure " }{TEXT 0 8 "areaplot" }{TEXT -1 10 " to work. " }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 27 "areaplot: implementation " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "areaplot" {MPLTEXT 1 0 12919 "areaplot : = proc(fx,eqn::equation)\n\n local x,y,xrange,yrange,rs,i,j,x1,x2,x3 ,xmax,xmin,p,instructions,\n curve,data,roots,xi,yi,xp,yp,xvals,x a,ya,xb,yb,startoptions,\n t1,t2,lbls,clr,aclr,bclr,curves,polygo ns,start,crv,h,k,frms,\n xcoord,polygon,Options,zrs,ars,line1,lin e2,anim,seqn,frame,\n signedareas,saveDigits,pgn,areafcn,subcrv,p t,intcrv,\n areagraph,num,fn,intf,convertopolygons,findmaxmins,\n t,u,rt,area,tp,lght,bstyle,acc,eps,haveroot,n;\n\n if not assi gned(`type/color`) or not assigned(lighten) then\n error \"the pr ocedure, %1, requires the type 'color' to be defined and also uses the procedure 'lighten' among the utility routines which enhance Maple's \+ colours\",'procname';\n end if;\n \n # Collect all the input dat a.\n x := lhs(eqn);\n if not type(x,name) then\n error \"2nd \+ argument equation left side, %1, must be the independent variable\",x; \n end if;\n if not type(indets(fx,name) minus \{x\},set(realcons) ) then\n error \"1st argument must depend only on %1, or be a rea l constant\",x;\n end if;\n \n rs := rhs(eqn);\n if type(rs,ra nge) then\n x1 := evalf(lhs(rs));\n x3 := evalf(rhs(rs));\n \+ xmin := x1;\n xmax := x3;\n xrange := xmin..xmax; # Plo tting interval same as area interval\n elif type(rs,list) then\n \+ if type(rs[1],range) then\n x1 := evalf(lhs(rs[1]));\n \+ x3 := evalf(rhs(rs[1]));\n end if;\n if type(rs[2],range) then\n xrange := evalf(rs[2])\n else\n error \"2 nd argument equation right side, %1, must be a range of real values or a list of two ranges\",rs;\n end if;\n xmin := evalf(lhs(rs [2]));\n xmax := evalf(rhs(rs[2])); \n if not type(xmin,re alcons) or not type(xmax,realcons) then\n error \"end points o f horizontal plotting range must be real constants\"\n end if;\n \+ if xmin>=xmax then\n error \"horizontal plotting range is invalid\"\n end if;\n end if;\n\n if not type(x1,realcons) o r not type(x3,realcons) then\n error \"end points of range for ar ea must be real constants\"\n end if;\n if x1>=x3 then\n erro r \"range for area is invalid\"\n end if;\n if not (xmin<=x1 and x max>=x3) then\n error \"range for area must be a subrange of the \+ plotting range\"\n end if;\n\n startoptions := 3; \n yrange := \+ NULL;\n if nargs>2 then \n if type(args[3],range) or type(args[ 3],name=range) then\n yrange := args[3];\n startoption s := 4;\n end if;\n end if;\n \n # Get the allowed options. \n Options := [];\n clr := [red,blue,green];\n aclr := [COLOR(RG B,1.,.8,.8),COLOR(RGB,.8,.8,1)];\n bclr := COLOR(RGB,.3,.3,.3);\n \+ frms := 30;\n zrs := false;\n ars := false;\n anim := false;\n \+ areafcn := false;\n num := false;\n bstyle := 1;\n if nargs>=st artoptions then\n Options:=[args[startoptions..nargs]];\n if not type(Options,list(equation)) then\n error \"each optional argument must be an equation\"\n end if;\n if hasoption(Opt ions,'zeros','zrs','Options') then\n if zrs<>true then zrs := \+ false end if;\n end if;\n if hasoption(Options,'areas','ars' ,'Options') then\n if ars<>true then ars := false end if;\n \+ end if;\n if hasoption(Options,'animation','anim','Options') t hen \n if anim<>true then anim := false end if;\n end if; \n if hasoption(Options,'areafunction','areafcn','Options') then \n if areafcn<>true then areafcn := false end if;\n end i f;\n if hasoption(Options,'numerical','num','Options') then\n \+ if num<>true then num := false end if;\n end if;\n if h asoption(Options,frames,'frms','Options') then\n if not type(f rms,posint) or frms<2 then\n error \"\\\"frames\\\" must be an integer greater than 1\"\n end if;\n end if;\n i f hasoption(Options,'color','tp','Options') or \n hasoption(Op tions,'colour','tp','Options') then\n if type(tp,list(color)) \+ then\n for j to min(nops(clr),nops(tp))\n do \+ clr[j] := tp[j] end do;\n elif type(tp,color) then\n \+ clr[1] := tp;\n clr[2] := tp;\n else\n \+ error \"color option must be single colour or a list of colours\"\n \+ end if;\n aclr := lighten(clr[1..2],.8);\n end if; \n if hasoption(Options,'shading','tp','Options') then\n \+ if type(tp,list(color)) then\n for j to min(nops(aclr),nops (tp))\n do aclr[j] := tp[j] end do;\n elif type( tp,color) then\n aclr[1] := tp;\n aclr[2] := tp; \n elif tp='lighten' then\n lght := .8;\n e lif type(tp,'lighten'[numeric]) then\n lght := evalf(op(1,t p));\n if lght<0 or lght>1 then\n error \"whe n the option \\\"shading\\\" has the form 'light[t]', the parameter t \+ should be between 0 and 1 .. current value of t is %1\",lght;\n \+ end if;\n else\n error \"the option \\\"shadin g\\\" must be single colour, a list of colours, or have the form 'ligh ten[t]' where t is between 0 and 1\"\n end if;\n end if; \n if hasoption(Options,'ord_color','bclr','Options') or\n \+ hasoption(Options,'ord_colour','bclr','Options') then\n if no t type(bclr,color) then\n error \"the ordinate colour optio n must be a single color\"\n end if;\n end if;\n if \+ hasoption(Options,'ord_style','bstyle','Options') then\n if no t type(bstyle,posint) or bstyle<1 or bstyle>4 then\n error \+ \"the linestyle for the ordinates must be an integer between 1 and 4\" \n end if;\n end if;\n end if;\n\n if assigned(lght) \+ then aclr := lighten(clr[1..2],lght) end if;\n\n if areafcn=true the n anim := true end if;\n \n # Use turning points to obtain a subdi vision into convex polygons.\n findmaxmins := proc(fx,x,data::listli st)\n local i,maxmins,direction,prevdirection;\n maxmins := \+ NULL;\n prevdirection := 0;\n for i from 1 to nops(data)-1 d o\n if data[i+1,2]>=data[i,2] then\n direction := 1 ;\n elif data[i+1,2]xb then break end if;\n incrv := incrv,crv[i]\n end do;\n \+ start := i; \n if (ya-yb)*sign>=0 then\n pg n := [[xa,0],[xa,ya],incrv,[xb,yb],[xb,0]];\n else\n \+ pgn := [[xb,0],[xa,0],[xa,ya],incrv,[xb,yb]];\n end if;\n\n \+ if sign>0 then\n polygon :=\n POLYGONS (pgn,STYLE(PATCHNOGRID),`plot/color`(aclr[1]));\n else\n \+ polygon :=\n POLYGONS(pgn,STYLE(PATCHNOGRID),`plot/c olor`(aclr[2]));\n end if;\n polygons := polygons,poly gon;\n end do;\n polygons;\n end proc: # of convertopolygo ns\n\n # Extract the plot data\n p := plot(fx,x=xrange,yrange,op(O ptions));\n instructions := seq(op(i,p),i=2..nops(p));\n curve := \+ op(1,p);\n data := op(1,curve);\n \n fn := evalf@unapply(fx,x); \n if areafcn=true then\n if num=true then\n intf := ev alf@unapply(Int(fn(t),t=x1..u),u);\n else\n intf := evalf @unapply(int(fn(t),t=x1..u),u);\n end if;\n p := plot(intf(x ),x=x1..x3);\n intcrv := op(1,op(1,plot(intf(x),x=x1..x3)));\n \+ end if;\n\n saveDigits := Digits;\n Digits := 15;\n\n # Get a li st of zeros in the plotting range.\n if type(fx,polynom) then \n \+ roots := op(sort([op(\{fsolve(fx,x=xrange)\})]));\n else\n ro ots := NULL;\n eps := max(seq(abs(data[i,2]),i=1..nops(data)))*Fl oat(1,-3);\n n := nops(data);\n for i from 1 to n-1 do\n \+ xi := data[i,1];\n yi := data[i,2];\n yp := data[ i+1,2];\n if yi=0 then\n roots := roots,xi;\n \+ elif yi*yp<0 or abs(yi)lasterror and type(rt,float);\n \+ if not haveroot then\n rt := traperror(fsolve(fx,x=( xi+xp)/2));\n haveroot := rt<>lasterror and type(rt,floa t);\n end if;\n if haveroot then\n \+ if xi<=rt and rtxb then break end if;\n crv := crv,data[i]\n end do;\n start := i;\n ya := fn(xa);\n yb := fn( xb);\n if xa=x1 then\n line1 := CURVES([[xa,0],[xa, ya]],\n `plot/color`(bclr),THICKNESS(1),LI NESTYLE(bstyle))\n end if;\n if xb=x2 then\n \+ line2 := CURVES([[xb,0],[xb,yb]],\n `plo t/color`(bclr),THICKNESS(1),LINESTYLE(bstyle))\n end if;\n \+ crv := [xa,ya],crv,[xb,yb];\n if xb<=x1 or xa>=x2 then\n \+ # Don't colour area at ends \n if evalf(eval(sub s(x=(xa+xb)/2,fx)))>0 then \n curve := CURVES([crv],`plo t/color`(clr[1]));\n else\n curve := CURVES([ crv],`plot/color`(clr[2]));\n end if;\n curves : = curves,curve;\n else\n if ars=true then\n \+ if num=true then\n area := traperror(evalf(Int (fx,x=xa..xb),saveDigits));\n if area<>lasterror and \+ type(area,float) then \n signedareas := signedarea s,area\n else\n WARNING(\"could n ot calculate area in interval %1 to %2\",xa,xb);\n en d if;\n else\n area := traperror(evalf( int(fx,x=xa..xb),saveDigits));\n if area<>lasterror a nd type(area,float) then \n signedareas := signeda reas,area\n else\n WARNING(\"coul d not calculate area in interval %1 to %2\",xa,xb);\n \+ end if;\n end if; \n end if;\n if evalf(eval(subs(x=(xa+xb)/2,fx)))>0 then\n curve := CUR VES([crv],`plot/color`(clr[1]));\n polygon := convertopo lygons(fx,x,[crv],1);\n else\n curve := CURVE S([crv],`plot/color`(clr[2]));\n polygon := convertopoly gons(fx,x,[crv],-1);\n end if;\n polygons := pol ygons,polygon;\n curves := curves,curve;\n end if; \n end do;\n if areafcn=true then\n subcrv := NULL; \n acc := `plot/color`(clr[3]);\n for i from 1 to nops (intcrv) do\n if intcrv[i,1]>x2 then break end if;\n \+ subcrv := subcrv,intcrv[i];\n end do;\n pt := [x2 ,intf(x2)];\n subcrv := subcrv,pt;\n areagraph := CURV ES([subcrv],acc),POINTS(pt,acc);\n frame := PLOT(curves,polyg ons,line1,line2,\n areagraph,instructions );\n else\n frame := PLOT(curves,polygons,line1,line2,ins tructions);\n end if;\n if anim=true then seqn := seqn,frame end if;\n end do;\n Digits := saveDigits;\n if ars = true then \n print(`signed areas ... `,signedareas);\n end if;\n if an im=true then\n plots[display]([seqn],insequence=true);\n else\n frame;\n end if;\nend proc: # of areaplot" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "Examples are gi ven in the next section." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 30 "Utility routines for colours: " }{TEXT 0 32 "ShowColours, convert(..,RGB) etc." }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 135 "Reference: \"Computer Graphics, Princi ples and Practice\" by Foley, van Dam, Feiner, and Hughes,\n Addison Wesley, Second Edition, 1990." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "ShowColours: usage" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 269 18 "Calling Sequence:\n" }}{PARA 0 "" 0 "" {TEXT -1 26 " ShowCo lours( clr, n ) " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 11 "Parameters:" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 98 " clr - a colour, which can be a named c olour or be specified in RGB, HSV or HLS format. " }}{PARA 0 "" 0 "" {TEXT -1 76 " This argument may also be a positive in teger, or \"all\". " }}{PARA 0 "" 0 "" {TEXT -1 98 " n - \+ a positive integer giving the number of colours 'similar' to clr to be displayed. " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 256 "" 0 "" {TEXT -1 12 "Description:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 14 "The procedure " }{TEXT 0 11 "ShowColours" }{TEXT -1 40 " displays colours available for plots. ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 21 "lighten,darken: \+ usage" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }{TEXT 268 18 "Calling Sequence:\n" }}{PARA 0 "" 0 "" {TEXT -1 42 " \+ lighten( clr )\n lighten( clr, t ) " }}{PARA 0 "" 0 "" {TEXT -1 40 " darken( clr )\n darken( clr, t ) " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 11 "Parameters:" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 101 " clr - a colour, which can be a named colour or be specified in RGB, HSV o r HLS format. " }}{PARA 0 "" 0 "" {TEXT -1 88 " t - a pa rameter which evaluates to a floating point number between 0 and 1. " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 256 "" 0 "" {TEXT -1 12 "Desc ription:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "The procedures " }{TEXT 0 14 "lighten,darken" }{TEXT -1 102 " ligh ten and darken by an amount which can be controlled using the 2nd opti onal parameter if desired. " }}{PARA 0 "" 0 "" {TEXT -1 57 "When the c olour is given in terms of its HLS components, " }{TEXT 0 7 "lighten" }{TEXT -1 33 " changes the lightness component " }{TEXT 270 1 "L" } {TEXT -1 4 " to " }{XPPEDIT 18 0 "L*`'`" "6#*&%\"LG\"\"\"%\"'GF%" } {TEXT -1 8 ", where " }{XPPEDIT 18 0 "L*`'` = t +(1-t)*L" "6#/*&%\"LG \"\"\"%\"'GF&,&%\"tGF&*&,&F&F&F)!\"\"F&F%F&F&" }{TEXT -1 8 ", while " }{TEXT 0 6 "darken" }{TEXT -1 33 " changes the lightness component " } {TEXT 271 1 "L" }{TEXT -1 4 " to " }{XPPEDIT 18 0 "L*`'`" "6#*&%\"LG\" \"\"%\"'GF%" }{TEXT -1 8 ", where " }{XPPEDIT 18 0 "L*`'` = (1-t)*L" " 6#/*&%\"LG\"\"\"%\"'GF&*&,&F&F&%\"tG!\"\"F&F%F&" }{TEXT -1 2 ". " }} {PARA 0 "" 0 "" {TEXT -1 14 "The parameter " }{TEXT 272 1 "t" }{TEXT -1 27 " has the default value of " }{XPPEDIT 18 0 "1/3" "6#*&\"\"\"F$ \"\"$!\"\"" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 264 16 "How to activat e:" }{TEXT 256 1 "\n" }{TEXT -1 163 "To make procedures active open th e appropriate subsection, place the cursor anywhere after the prompt [ > and press [Enter].\nYou can then close up the subsection." }} {PARA 0 "" 0 "" {TEXT 264 4 "Note" }{TEXT -1 242 ": In order for a pro cedure in this list to work it may be necessary for a preceding proced ure to be active, that is, if you load selectively, you should be awar e of possible depedencies on preceding procedures as you go down throu gh the list." }}{PARA 0 "" 0 "" {TEXT -1 27 "For example, the procedur e " }{TEXT 0 11 "ShowColours" }{TEXT -1 36 " requires the conversion p rocedures " }{TEXT 0 15 "convert(..,RGB)" }{TEXT -1 2 ", " }{TEXT 0 15 "convert(..,HSV)" }{TEXT -1 2 ", " }{TEXT 0 15 "convert(..,HLS)" } {TEXT -1 17 " to be active. " }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 48 "type(..,colour), type(..,color): implementation " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 478 "`type/colou r` := proc(cc)\n if type(cc,function) and member(op(0,cc),\{'COLOR', 'COLOUR'\}) then\n if member(op(1,cc),\{'RGB','HSV','HLS'\}) and \+ nops(cc)=4 \n and type([op(2..4,cc)],list(numeric)) then true\n elif op(1,cc)='HUE' and nops(cc)=2 \n and type(op(2,cc),n umeric) then true\n else false end if;\n else \n try\n \+ `plot/color`(cc);\n true;\n catch: false;\n end try;\n end if;\nend proc:\n`type/color` := eval(`type/colour`):" }} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 64 "convert(..,RGB), convert(..,HSV),convert(..,HLS): implementation" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6790 "`convert/RGB` := proc(cc)\n local h,s,v,synOK,clr,i,f,p,q,t,l, r,g,b;\n\n if type(cc,\{list,set\}) then \n return map('procnam e',cc)\n end if;\n\n clr := cc;\n\n if type(clr,function) and me mber(op(0,clr),\{'COLOR','COLOUR'\}) then\n if member(op(1,clr), \{'RGB','HSV','HLS'\}) and nops(clr)=4 \n and type([op(2..4,clr )],list(numeric)) then synOK := true\n elif op(1,clr)='HUE' and n ops(clr)=2 \n and type(op(2,clr),numeric) then synOK := true\n \+ else synOK := false end if;\n else\n synOK := false\n en d if; \n\n if synOK then\n if op(1,clr)='RGB' then\n\011 \+ r := max(min(evalf(op(2,clr)),1.),0.);\n\011 g := max(min(eval f(op(3,clr)),1.),0.);\n \011 b := max(min(evalf(op(4,clr)),1.),0 .);\n return COLOR(RGB,r,g,b);\n elif op(1,clr)='HUE' the n\n h := evalf(op(2,clr));\n h := h-floor(h);\n \+ clr := COLOR(HSV,h,0.9,1.0)\n end if;\n end if;\n\n if not \+ synOK then\n try\n clr := `plot/color`(clr);\n re turn clr; \n catch: error \"unable to convert %1 to an RG B colour\",clr;\n end try;\n end if;\n\n Digits := 8;\n if \+ op(1,clr)='HSV' then\n\011 h := evalf(op(2,clr));\n h := h-fl oor(h);\n\011 s := max(min(evalf(op(3,clr)),1.),0.);\n \011 v : = max(min(evalf(op(4,clr)),1.),0.);\n h := h*6;\n i := floor (h);\n\011 \011\011f := h-i;\n\011 \011 p := v*(1-s);\n\011 \011 q := v*(1-s*f) ;\n\011 \011 t := v*(1-s*(1-f));\n \n \011\011 if i=0 then\n COLOR('RGB',v,t,p)\n\011\011\011 elif i=1 the n\n\011\011\011 COLOR('RGB',q,v,p)\n elif i=2 then\n \+ COLOR('RGB',p,v,t)\n elif i=3 then\n COLOR('RGB',p,q,v) \n elif i=4 then\n COLOR('RGB',t,p,v)\n\011\011\011 els e # i=5 then\n COLOR('RGB',v,p,q)\n end if;\n else # op (1,clr)='HLS'\n\011 h := evalf(op(2,clr));\n h := h-floor(h); \n\011 l := max(min(evalf(op(3,clr)),1.),0.);\n \011 s := max(m in(evalf(op(4,clr)),1.),0.);\n h := h*6;\n p := `if`(l<=.5,l +l*s,l+s-l*s);\n q := 2*l-p;\n t := p-q;\n if s=0 then \n COLOR('RGB',l,l,l);\n else\n if h<1 then\n \+ COLOR('RGB',p,q+t*h,q)\n elif h<2 then\n CO LOR('RGB',q+t*(2-h),p,q)\n elif h<3 then\n COLOR('R GB',q,p,q+t*(h-2))\n elif h<4 then \n COLOR('RGB',q ,q+t*(4-h),p)\n elif h<5 then\n COLOR('RGB',q+t*(h- 4),q,p)\n else\n COLOR('RGB',p,q,q+t*(6-h))\n \+ end if;\n end if;\n end if;\nend proc: # `convert/RGB`\n\n`c onvert/HSV` := proc(cc)\n local clr,synOK,r,g,b,h,s,v,d,l,u,t;\n\n \+ if type(cc,\{list,set\}) then \n return map('procname',cc)\n e nd if;\n\n clr := cc;\n if type(clr,function) and member(op(0,clr) ,\{'COLOR','COLOUR'\}) then\n if member(op(1,clr),\{'RGB','HSV',' HLS'\}) and nops(clr)=4 \n and type([op(2..4,clr)],list(numeric )) then synOK := true\n elif op(1,clr)='HUE' and nops(clr)=2 \n \+ and type(op(2,clr),numeric) then synOK := true\n else synOK := false end if;\n else\n synOK := false\n end if;\n\n if \+ synOK then\n if op(1,clr)='HSV' then\n\011 h := evalf(op(2 ,clr));\n h := h-floor(h);\n\011 s := max(min(evalf(op( 3,clr)),1.),0.);\n \011 v := max(min(evalf(op(4,clr)),1.),0.);\n return COLOR('HSV',h,s,v);\n elif op(1,clr)='HUE' then\n \011 h := evalf(op(2,clr));\n h := h-floor(h);\n \+ return COLOR('HSV',h,0.9,1.0);\n end if;\n end if;\n\n if n ot synOK then\n try clr := `plot/color`(clr);\n catch: error \"unable to convert %1 to an HSV colour\",clr;\n end try;\n en d if;\n\011\n Digits := 8;\n if op(1,clr)='RGB' then\n\011 r : = max(min(evalf(op(2,clr)),1.),0.);\n\011 g := max(min(evalf(op(3, clr)),1.),0.);\n \011 b := max(min(evalf(op(4,clr)),1.),0.);\n\n \+ v := max(r,g,b); \n d := v-min(r,g,b);\n if d=0 then # r = g = b\n return COLOR('HSV',evalf(2/3),0.,r);\n end i f;\n\n s := d/v; \n\011 if v=r then\n\011\011 h := (g -b)/d;\011# between yellow & magenta\n\011 elif v=g then\n\011\011 h := 2+(b-r)/d;\011# between cyan & yellow\n\011 else\n\011 \011 h := 4+(r-g)/d;\011# between magenta & cyan\n end if; \n h := h/6;\n\011 if h<0 then h := h+1. end if;\n COLOR ('HSV',h,s,v);\n else # op(1,clr)=HLS\n\011 h := evalf(op(2,clr) );\n h := h-floor(h);\n\011 l := max(min(evalf(op(3,clr)),1.) ,0.);\n \011 s := max(min(evalf(op(4,clr)),1.),0.);\n u := 2*l ;\n d := `if`(u<1,u*s,(2-u)*s);\n t := u+d;\n v := t/2; \n s := `if`(v<>0,d/v,0.);\n COLOR('HSV',h,s,v);\n end if; \nend proc: # `convert/HSV`\n\n`convert/HLS` := proc(cc)\n local clr ,synOK,r,g,b,h,s,l,d,u,v,m;\n\n if type(cc,\{list,set\}) then \n \+ return map('procname',cc)\n end if;\n\n clr := cc;\n if type(c lr,function) and member(op(0,clr),\{'COLOR','COLOUR'\}) then\n if member(op(1,clr),\{'RGB','HSV','HLS'\}) and nops(clr)=4 \n and type([op(2..4,clr)],list(numeric)) then synOK := true\n elif op( 1,clr)='HUE' and nops(clr)=2 \n and type(op(2,clr),numeric) the n synOK := true\n else synOK := false end if;\n else\n syn OK := false\n end if;\n\n if synOK then\n if op(1,clr)='HLS' \+ then\n\011 h := evalf(op(2,clr));\n h := h-floor(h);\n \011 l := max(min(evalf(op(3,clr)),1.),0.);\n \011 s := m ax(min(evalf(op(4,clr)),1.),0.);\n return COLOR(HSV,h,l,s);\n \+ elif op(1,clr)='HUE' then\n\011 h := evalf(op(2,clr));\n \+ h := h-floor(h);\n return COLOR('HLS',h,0.55,1.0);\n \+ end if;\n end if;\n\n if not synOK then\n try clr := `plot /color`(clr);\n catch: error \"unable to convert %1 to an HLS col our\",clr;\n end try;\n end if;\n\011\n Digits := 8;\n if o p(1,clr)='RGB' then\n\011 r := max(min(evalf(op(2,clr)),1.),0.);\n \011 g := max(min(evalf(op(3,clr)),1.),0.);\n \011 b := max(min (evalf(op(4,clr)),1.),0.);\n\n # compute the lightness\n v : = max(r,g,b);\n m := min(r,g,b);\n u := v+m;\n d := v-m ;\n l := u/2;\n\n if d=0 then # r = g = b\n return COLOR('HLS',evalf(2/3),l,0.);\n end if;\n\n # compute the H LS saturation\n s := `if`(l<=.5,d/u,d/(2-u));\n\n # compute \+ the hue\n\011 if v=r then\n\011\011 h := (g-b)/d;\011# betwe en yellow & magenta\n\011 elif v=g then\n\011\011 h := 2+(b- r)/d;\011# between cyan & yellow\n\011 else\n\011\011 h := 4 +(r-g)/d;\011# between magenta & cyan\n end if;\n h := h/6; \n if h<0 then h := h+1. end if;\n COLOR('HLS',h,l,s);\n e lse # op(1,clr)=HSV\n\011 h := evalf(op(2,clr));\n h := h-flo or(h);\n\011 s := max(min(evalf(op(3,clr)),1.),0.);\n \011 v := max(min(evalf(op(4,clr)),1.),0.);\n d := s*v;\n m := v-d;\n u := v+m;\n l := u/2;\n\n # compute the HLS saturation \n if d=0 then\n s := 0.\n else\n s := `if`( l<=.5,d/u,d/(2-u));\n end if;\n COLOR('HLS',h,l,s); \n end if;\nend proc: # `convert/HLS`" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 27 "ShowColours: implementation" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2853 "ShowColours := proc(ff)\n local i,clrs,clrnames,cc,ci,t,h,pp,r ect,txt,start,finish,\n jF,jS,jM,n,c1,k,j,under,over,ord;\n\n c lrnames := map(op,[indices(`plot/colortable`)]);\n cc := [];\n for i to nops(clrnames) do\n ci := clrnames[i];\n if not String Tools[IsUpper](ci) then\n t := COLOR(RGB,op(`plot/colortable` [ci]));\n h := convert(t,HSV);\n cc := [op(cc),[op(2 ..4,h),ci,t]]\n end if;\n end do;\n ord := proc(_u,_v)\n \+ if op(1,_u)1 do\n jM := trunc((jF+jS)/2); \n if not ord(h,cc[jM]) then jF := jM \n else jS := jM end if;\n end do;\n end if;\n\n if nargs>=2 a nd type(args[2],posint) then \n k := iquo(min(args[2],n),2);\n else\n k := 5;\n end if;\n under := min(n+jF-k ,n);\n start := max(jF-k,1);\n finish := min(jF+k,n);\n \+ over := max(jF+k-n,1);\n end if;\n\n pp := NULL;\n j := 1;\n \+ if under1 then\n for i from 1 to ove r do\n rect := plots[polygonplot]([[0,1-j],[1,1-j],[1,-j],[0,- j]],\n style=patchnogrid,color=op(4,cc[i]));\n tx t := plots[textplot]([1.2,0.5-j,op(4,cc[i])],color=black,align=RIGHT); \n pp := pp,plots[display]([rect,txt]);\n j := j+1;\n \+ end do;\n end if;\n plots[display]([pp],axes=NONE);\nend proc : # ShowColours" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 31 "lighten, dar ken: implementation" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2775 "lighten := proc(cc::\{color,list(color),s et(color)\})\n local c,r,c2,drw,optn,p1,p2;\n\n if type(cc,\{list, set\}) then \n return map('procname',cc,args[2..nargs])\n end i f;\n\n if op(1,cc)='HLS' then\n c := cc;\n else\n c := c onvert(cc,'HLS'); \n end if; \n\n Digits := 8;\n if nargs>1 \+ and type(args[2],numeric) then\n r := evalf(args[2]);\n if r >1 or r<0 then\n error \"expecting the 2nd argument to evaluat e to a floating point number between 0 and 1, but received %1\",args[2 ];\n end if;\n else\n r := evalf(1/3);\n end if;\n\n i f nargs=2 and not type(args[2],numeric) then\n optn := args[2]\n \+ elif nargs=3 then\n optn := args[3]\n end if;\n\n drw := fa lse;\n if assigned(optn) then\n if type(optn,`=`) then \n \+ if op(1,optn)=draw then drw := op(2,optn) end if;\n if drw< >true then drw := false end if;\n elif optn=draw then drw := true ;\n end if;\n end if; \n \n # increase the 'L' component t owards 1\n c2 := COLOR(HLS,op(2,c),r+(1-r)*op(3,c),op(4,c));\n if \+ drw then\n p1 := plots[polygonplot]([[0,0],[1,0],[1,1],[0,1]],col or=c);\n p2 := plots[polygonplot]([[0,0],[1,0],[1,-1],[0,-1]],col or=c2);\n print(plots[display]([p1,p2],axes=NONE));\n end if;\n if op(1,cc)='RGB' then\n convert(c2,'RGB')\n elif op(1,cc)=' HSV' then\n convert(c2,HSV)\n else c2 end if;\nend proc: # of l ighten\n\ndarken := proc(cc::\{color,list(color),set(color)\})\n loc al c,r,c2,drw,optn,p1,p2;\n\n if type(cc,\{list,set\}) then \n \+ return map('procname',cc,args[2..nargs])\n end if;\n\n if op(1,cc) ='HLS' then\n c := cc;\n else\n c := convert(cc,'HLS'); \+ \n end if; \n\n Digits := 8;\n if nargs>1 and type(args[2],num eric) then\n r := evalf(args[2]);\n if r>1 or r<0 then\n \+ error \"expecting the 2nd argument to evaluate to a floating poin t number between 0 and 1, but received %1\",args[2];\n end if;\n \+ else\n r := evalf(1/3);\n end if;\n\n if nargs=2 and not ty pe(args[2],numeric) then\n optn := args[2]\n elif nargs=3 then \n optn := args[3]\n end if;\n\n drw := false;\n if assigne d(optn) then\n if type(optn,`=`) then \n if op(1,optn)=dr aw then drw := op(2,optn) end if;\n if drw<>true then drw := f alse end if;\n elif optn=draw then drw := true;\n end if;\n \+ end if;\n\n # decrease the 'L' component towards 0\n c2 := COLOR (HLS,op(2,c),(1-r)*op(3,c),op(4,c));\n if drw then\n p1 := plot s[polygonplot]([[0,0],[1,0],[1,1],[0,1]],color=c);\n p2 := plots[ polygonplot]([[0,0],[1,0],[1,-1],[0,-1]],color=c2);\n print(plots [display]([p1,p2],axes=NONE));\n end if;\n if op(1,cc)='RGB' then \n convert(c2,'RGB')\n elif op(1,cc)='HSV' then\n convert( c2,HSV)\n else c2 end if;\nend proc: # of darken" }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 63 "`plot/color`: \+ implementation (replacement for default version) " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1197 "`plot/colo r` := proc(t)\n local h,l,s,u,d,w,v;\n if type(t,function) and (op (0,t)='COLOUR' or op(0,t)='COLOR') then\n if member(op(1,t),\{'HL S','HSV'\}) then \n if nops(t)=4 and type([op(2..4,t)],list(nu meric)) then\n h := op(2,t);\n h := h-floor(h); \n if op(1,t)='HSV' then\n COLOUR('HSV',h,op( 3..4,t))\n else # convert HLS to HSV\n\011 l : = max(min(op(3,t),1),0);\n \011 s := max(min(op(4,t),1),0) ;\n u := 2*l;\n d := `if`(u<1,u*s,(2-u)*s) ;\n w := u+d;\n v := w/2;\n \+ s := `if`(v<>0,d/v,0.);\n COLOUR('HSV',h,s,v);\n \+ end if\n else error \"invalid HSV or HLS COLOUR data\"\n \+ end if\n elif op(1,t)='HUE' then\n if nops(t)=2 an d type(op(2,t),numeric) then\n h := op(2,t);\n h := h-floor(h);\n COLOUR('HUE',h);\n else error \"i nvalid HUE COLOUR data\"\n end if;\n else t end if;\n elif member(t,map(op,\{indices(`plot/colortable`)\})) then\n COLOUR(' RGB',op(`plot/colortable`[t]))\n else error \"invalid color specific ation\"\n end if\nend proc: # of `plot/color`" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 52 "`plot/colortable `: replacement for default version " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6796 "`plot/colortable` := \n \+ table(\n # colours retained from default table\n [gold=[.800,.49 8,.196],\n blue=[0.,0.,1.], \n magenta=[1.,0.,1.],\n white=[1., 1.,1.],\n pink=[1.,.753,.796],\n cyan=[0.,1.,1.],\n sienna=[.557 ,.42,.137],\n aquamarine=[.439,.859,.576],\n maroon=[.557,.137,.42 ],\n yellow=[1.,1.,0.],\n green=[0.,1.,0.],\n navy=[.137,.137,.5 57],\n khaki=[.624,.624,.373],\n grey=[.753,.753,.753],\n red=[1 .,0.,0.],\n plum=[.918,.678,.918],\n black=[0,0,0],\n turquoise= [.678,.918,.918],\n brown=[.647,.165,.165],\n tan=[.859,.576,.439] ,\n wheat=[.961,.871,.702],\n coral=[1.,.498,0.],\n\n # more col ours\n bright_gold=[.851,.851,.098],\n brass=[.710,.651,.259],\n \+ grey_bronze=[.549,.471,.325],\n cool_copper=[.851,.529,.098],\n b ronze=[.651,.490,.239],\n spicy_pink=[1.,.11,.682],\n dark_chocola te=[.42,.259,.149],\n scarlet=[.549,.0902,.0902],\n light_tan=[.92 2,.78,.62],\n silver=[.902,.91,.98],\n light_grey=[.804,.804,.804] ,\n old_gold=[.812,.710,.231],\n mandarin_orange=[.894,.471,.2],\n neon_pink=[1.,.431,.78],\n neon_blue=[.302,.302,1.],\n copper=[ .722,.451,.2],\n light_green=[.565,.933,.565],\n very_dark_brown=[ .361,.251,.200],\n\n # even more colours\n alice_blue=[.941,.973,1 .],\n alizarin_crimson=[.889,.15,.21],\n antique=[.981,.922,.845], \n cyan_aquamarine=[.47, .93, .65],\n medium_aquamarine=[.4,.804,. 667],\n aureoline_yellow=[1.,.66,.14],\n azure=[.942,1.,1.],\n b anana=[.89,.81,.34],\n beige=[.64,.58,.5],\n bisque=[1.,.898,.772] ,\n blanched_almond=[1.,.923,.804],\n light_blue=[0,.45,1.],\n p ale_blue=[.678,.847,.902],\n medium_blue=[0.,0.,.804],\n blue_viol et=[.541,.169,.886],\n brick=[.61,.4,.12],\n brown=[.5,.165,.165], \n brown_oadder=[.86,.16,.16],\n brown_ochre=[.53,.26,.12],\n bu rlywood=[.871,.722,.529],\n burnt_sienna=[.54,.21,.06],\n burnt_um ber=[.54,.2,.14],\n cadet=[.372,.62,.628],\n cadmium_lemon=[1.,.89 ,.01],\n cadmium_orange=[1.,.38,.01],\n deep_cadmium_red=[.89,.09, .05],\n light_cadmium_red=[1.,.01,.05],\n cadmium_yellow=[1.,.6,.0 7],\n light_cadmium_yellow=[1.,.69,.06],\n carrot=[.93,.57,.13],\n cerulean=[.02,.72,.8],\n chartreuse=[.498,1.,0.],\n chocolate=[ .823,.412,.118],\n chrome_oxide_green=[.4,.5,.08],\n cinnabar_gree n=[.38,.7,.16],\n cobalt=[.24,.35,.67],\n cobalt_green=[.24,.57,.2 5],\n deep_cobalt_violet=[.57,.13,.62],\n cold_grey=[.5,.54,.53], \n pinkish_coral=[1.,.498,.314],\n coral_pink=[.941,.502,.502],\n \+ cornflower_blue=[.392,.584,.929],\n cornsilk=[1.,.973,.863],\n l ight_cyan=[.333,1.,1.],\n orange=[1.,.549,0.],\n deep_pink=[1.,.07 84,.576],\n deep_ochre=[.45,.24,.1],\n dim_grey=[.333333,.333333,. 333333],\n dodger_blue=[.118,.565,1.],\n eggshell=[.99,.9,.79],\n \+ emerald_green=[0.,.79,.34],\n english_red=[.83,.24,.1],\n firebr ick=[.698,.133,.133],\n flesh=[1.,.49,.25],\n flesh_ochre=[1.,.34, .13],\n floral=[1.,.98,.941],\n forest_green=[.133,.545,.133],\n \+ gainsboro=[.863,.863,.863],\n geranium_lake=[.89,.07,.19],\n gold _yellow=[1.,.843,0.],\n gold_ochre=[.78,.47,.15],\n goldenrod=[.85 5,.647,.126],\n dark_goldenrod=[.722,.525,.043],\n light_goldenrod =[.98,.98,.823],\n pale_goldenrod=[.933,.91,.667],\n dark_green=[0 .,.3927,0.],\n pale_green=[.596,.984,.596],\n green_yellow=[.678,1 .,.184],\n redish_umber=[1.,.24,.05],\n honeydew=[.941,1.,.941],\n hot_pink=[1.,.412,.706],\n indian_red=[.69,.09,.12],\n indigo=[ .03,.18,.33],\n ivory_black=[.16,.14,.13],\n pale_khaki=[.941,.902 ,.549],\n light_khaki=[.741,.718,.42],\n lamp_black=[.18,.28,.23], \n lavender=[.93,.902,.98],\n lawn_green=[.486,.988,0.],\n lemon _chiffon=[1.,.98,.804],\n light_beige=[.961,.961,.863],\n light_go ldenrod=[.933,.867,.51],\n medium_grey=[.667,.667,.667],\n dark_gr ey=[.58,.58,.58],\n light_salmon=[1.,.628,.478],\n lime_green=[.19 6,.804,.196],\n linen=[.98,.941,.902],\n deep_madder_lake=[.89,.18 ,.19],\n manganese_blue=[.01,.66,.62],\n maroon_red=[.69,.188,.377 ],\n mars_orange=[.59,.27,.08],\n mars_yellow=[.89,.44,.1],\n me lon=[.89,.66,.41],\n midnight_blue=[.098,.098,.439],\n mint=[.74,. 99,.79],\n misty_rose=[1.,.894,.882],\n moccasin=[1.,.894,.71],\n \+ deep_naples_yellow=[1.,.66,.07],\n navajo=[1.,.871,.678],\n navy _blue=[0.,0.,.502],\n old_lace=[.992,.961,.902],\n olive=[.23,.37, .17],\n drab_olive=[.42,.557,.137],\n dark_olive_green=[.333,.42,. 184],\n orange_red=[1.,.271,0.],\n orchid=[.855,.439,.839],\n da rk_orchid=[.6,.196,.8],\n medium_orchid=[.729,.333,.827],\n papaya _whip=[1.,.937,.835],\n peach=[.44,.26,.26],\n peach_puff=[1.,.855 ,.726],\n peacock=[.2,.63,.79],\n permanent_green=[.04,.79,.17],\n permanent_red_violet=[.86,.15,.27],\n peru=[.804,.522,.247],\n \+ light_pink=[1.,.804,.871],\n plum=[.867,.628,.867],\n light_plum=[ .918,.678,.918],\n powder_blue=[.69,.878,.902],\n prussian_blue=[. 18,.18,.31],\n purple=[.4,0,.9],\n medium_purple=[.628,.126,.941], \n slate_blue_purple=[.576,.439,.859],\n raspberry=[.53,.15,.34], \n raw_sienna=[.78,.38,.08],\n raw_umber=[.45,.29,.07],\n red_br ick=[.8,.196,.196],\n rose_madder=[.89,.21,.22],\n rosy_brown=[.73 7,.561,.561],\n royal_blue=[.255,.412,.882],\n saddle_brown=[.545, .271,.0745],\n salmon=[.98,.502,.447],\n sandy_brown=[.957,.643,.3 77],\n sap_green=[.19,.5,.089],\n sea_green=[.180,.545,.341],\n \+ dark_sea_green=[.561,.737,.561],\n light_sea_green=[.126,.698,.667], \n medium_sea_green=[.235,.702,.443],\n seashell=[1.,.961,.933],\n sepia=[.37,.15,.07],\n rich_sienna=[.628,.322,.177],\n sky_blue =[.529,.808,.922],\n deep_sky_blue=[0.,.749,1.],\n light_sky_blue= [.529,.808,.98],\n slate_blue=[.416,.353,.804],\n dark_slate_blue= [.282,.239,.545],\n light_slate_blue=[.518,.439,1.],\n medium_slat e_blue=[.482,.408,.933],\n slate_grey=[.439,.502,.565],\n dark_sla te_grey=[.184,.31,.31],\n light_slate_grey=[.467,.533,.6],\n smoke =[.961,.961,.961],\n spring_green=[0.,1.,.498],\n medium_spring_gr een=[0.,.98,.604],\n steel_blue=[.274,.51,.706],\n light_steel_blu e=[.69,.769,.871],\n terre_verte=[.22,.37,.06],\n thistle=[.847,.7 49,.847],\n titanium=[.99,1.,.94],\n tomato=[1.,.388,.278],\n tu rquoise=[.251,.878,.816],\n turquoise_blue=[0.,.78,.55],\n dark_tu rquoise=[0.,.808,.82],\n medium_turquoise=[.282,.82,.8],\n pale_tu rquoise=[.686,.933,.933],\n ultramarine=[.07,.04,.56],\n ultramari ne_violet=[.36,.14,.43],\n dark_brown=[.37,.15,.02],\n venetian_re d=[.83,.1,.12],\n violet=[.56,.37,.6],\n dark_violet=[.58,0.,.827] ,\n violet_red=[.816,.126,.565],\n medium_violet_red=[.78,.0824,.5 22],\n pale_violet_red=[.859,.439,.577],\n light_viridian=[.43,1., .44],\n warm_grey=[.5,.5,.41],\n yellow_brown=[.86,.58,.44],\n y ellow_green=[.604,.804,.196],\n light_yellow=[1.,1.,.878],\n yello w_ochre=[.89,.51,.09],\n zinc=[.87,.84,.89]]): # of `plot/colortable `" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 15 "For reference: " }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 29 "`plot/color`: default version" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 353 "`plot/color` := proc(t)\noption `Copyright (c) 1992 by the Univ ersity of Waterloo. All rights reserved.`;\n if type(t, function) a nd (op(0, t) = 'COLOUR' or op(0, t) = 'COLOR') then t\n elif member (t, map(op, \{indices(`plot/colortable`)\})) then COLOUR('RGB', op(`pl ot/colortable`[t]))\n else error \"invalid color specification\"\n \+ end if\nend proc:" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 " " {TEXT 0 8 "areaplot" }{TEXT -1 47 ": examples of regions enclosed be tween a graph " }{XPPEDIT 18 0 "y=f(x)" "6#/%\"yG-%\"fG6#%\"xG" } {TEXT -1 9 " and the " }{TEXT 288 1 "x" }{TEXT -1 7 " axis " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 9 "Example 1" }}{PARA 0 "" 0 "" {TEXT -1 64 "This example i llustrates the region enclosed between the graph " }{XPPEDIT 18 0 "y \+ = x^2-2*x;" "6#/%\"yG,&*$%\"xG\"\"#\"\"\"*&F(F)F'F)!\"\"" }{TEXT -1 9 " and the " }{TEXT 282 1 "x" }{TEXT -1 24 " axis over the interval " } {XPPEDIT 18 0 "[-1, 2];" "6#7$,$\"\"\"!\"\"\"\"#" }{TEXT -1 1 "." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 264 5 "Notes" } {TEXT -1 2 ": " }}{PARA 15 "" 0 "" {TEXT -1 89 "The 1st range is the i nterval the over which the area enclosed between the graph and the " } {TEXT 283 1 "x" }{TEXT -1 82 " axis is considered, while the 2nd range is the interval over which the graph of " }{XPPEDIT 18 0 "y = x^2-2* x;" "6#/%\"yG,&*$%\"xG\"\"#\"\"\"*&F(F)F'F)!\"\"" }{TEXT -1 13 " is pl otted. " }}{PARA 15 "" 0 "" {TEXT -1 65 "The 1st colour is for the seg ment of the graph cut off above the " }{TEXT 286 1 "x" }{TEXT -1 62 " \+ axis and the 2nd colour is for the segment cut off below the " }{TEXT 287 1 "x" }{TEXT -1 6 " axis." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "areaplot(x^2-2*x,x=[-1..3,-1 .2..3.2]);" }}{PARA 13 "" 1 "" {GLPLOT2D 357 321 321 {PLOTDATA 2 "6/-% 'CURVESG6$7'7$$!#7!\"\"$\"$%Q!\"#7$$!3%**************>\"!#<$\"3&)***** *******RQF17$$!3gmmm@D4/6F1$\"3?#fL(R`?FMF17$$!3QLLePRk?5F1$\"3+yA\\A> +$3$F17$$F*\"\"!$\"\"$F@-%'COLOURG6&%$RGBG$\"\"\"F@$F@F@FI-F$6$7/F>7$$ !3+mmmrF(zE*!#=$\"3?!)oHZxa7FF17$$!3vlmm,aGB$)FP$\"3]2$4\"zyUdBF17$$!3 gKL$e'z3$Q(FP$\"37'**yAZ<<-#F17$$!34mm;*e/9^'FP$\"3]S:2:[EEFP$\"3'*4&fvW$\"3gzcV-E!34#FP7$ $!3=^)*****\\:!H%!#?$\"3mEP#*Har)f)F^q7$FIFIFC-F$6$79Faq7$$\"3W9+++d5a ()Fhp$!3-IKRtn=u;FP7$$\"3hLL$3&fK4$4q #FP$!3'zbr#G1OsYFP7$$\"3Apmm'Q_4a$FP$!32+$pGRq!GeFP7$$\"3M,+](z&4=XFP$ !3A&Gh9js[*pFP7$$\"3Ynmm'GLIQ&FP$!3q*>(zO=OoyFP7$$\"3t-+](z1?L'FP$!3q \"QTme#ea')FP7$$\"32/+]#*RlNsFP$!3/$)=3:\"ReB*FP7$$\"3mpmmT]^y\")FP$!3 kUlla#>#o'*FP7$$\"37pm;9eNW!*FP$!3Q&H3!>Wn3**FP7$$\"3EMLLe?Gy**FP$!3#o (45LG&*****FP7$$\"3OLL3&*o$[4\"F1$!3@H&4Ljf+\"**FP7$$\"3I++DWKGz6F1$!3 A[>J$=v&y'*FP7$$\"3]LL$[h([q7F1$!3+Vx@-XOo#*FP7$$\"3C+++a1rk8F1$!3)>#* )e)Qh)p')FP7$$\"37++]:&*)oX\"F1$!3h`D\"zFP7$$\"3U++v.t2Y:F1$!3e(H \"H$y&*z,(FP7$$\"3-++]O^5X;F1$!3CjJhGORQeFP7$$\"3\\mmm[g3M=1EJFP7$$\"3iLL3F==:>F1$!3@6TwLAUC;FP7$ $\"\"#F@FI-FD6&FFFIFIFG-F$6$7/F^x7$$\"3P+++n0I4?F1$\"3=*=_YXj(o=Fhp7$$ \"3CmmTm*ey4#F1$\"3Q5ZT,J%H0#FP7$$\"3q++v5!G/>#F1$\"3+O?y([)=rTFP7$$\" 3[mmmr6$4G#F1$\"3@\"RtamYyS'FP7$$\"39++v$fzcP#F1$\"3=a;gYM%\\#*)FP7$$ \"3'QLL`eLpY#F1$\"3?4*yP9%*=:\"F17$$\"39ML$=(RDgDF1$\"3,&p@mX#RM9F17$$ \"3SnmT=;!Gl#F1$\"3*\\vS)*=`1$F17$$\"3j++D[sR/JF1$ \"3Bv@Wyx[GMF17$$\"3;+++++++KF1$\"3j,+++++SQF17$$\"#KF*F+FC-%)POLYGONS G6%737$F?F@F>F>FMFSFXFgnF\\oFaoFfoF[pF`pFepF[qFaqFaq7$FIF@-%&STYLEG6#% ,PATCHNOGRIDG-%&COLORG6&FFFG$\"\")F*F`^l-Fd]l6%727$FhtF@Fh]lFaqFaqFeqF jqF_rFdrFirF^sFcsFhsF]tFbtFgtFgtFi]l-F^^l6&FFF`^lF`^lFH-Fd]l6%71Fe^lFg tF\\uFauFfuF[vF`vFevFjvF_wFdwFiwF^xF^x7$F_xF@Fi]lFf^l-Fd]l6%737$FAF@F[ _lF^xF^xFfxF[yF`yFeyFjyF_zFdzFizF^[lFc[lFh[lF]\\lF]\\lFi]lF]^l-F$6&7$F g]lF>-F^^l6&FF$FBF*Fe_lFe_l-%*THICKNESSG6#FH-%*LINESTYLEGFh_l-F$6&7$F_ _lF]\\lFc_lFf_lFi_l-%+AXESLABELSG6$Q\"x6\"Q!Fb`l-%%VIEWG6$;F(Fa]l%(DEF AULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve \+ 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve \+ 8" "Curve 9" "Curve 10" "Curve 11" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Example 2" }}{PARA 0 "" 0 "" {TEXT -1 63 "This example \+ illustrates the region enclosed between the graph " }{XPPEDIT 18 0 "y \+ = x^4-2*x^2+1;" "6#/%\"yG,(*$%\"xG\"\"%\"\"\"*&\"\"#F)*$F'F+F)!\"\"F)F )" }{TEXT -1 9 " and the " }{TEXT 273 1 "x" }{TEXT -1 24 " axis over t he interval " }{XPPEDIT 18 0 "[-5/4, 5/4];" "6#7$,$*&\"\"&\"\"\"\"\"%! \"\"F)*&F&F'F(F)" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 264 4 "Note" }{TEXT -1 13 ": The colour " } {TEXT 285 10 "misty_rose" }{TEXT -1 50 " for the shading belongs to th e enhanced colours. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "areaplot(x^4-2*x^2+1,x=[-1.25..1.25,-1.4 5..1.45],\n color=brown,shading=misty_rose,ord_style=3);" }} {PARA 13 "" 1 "" {GLPLOT2D 478 302 302 {PLOTDATA 2 "6/-%'CURVESG6$7/7$ $!$X\"!\"#$\"*D1b@\"!\")7$$!3'*************\\9!#<$\"3z******\\i]:7F17$ $!3^m\"HK1(>M9F1$\"3[\">,sX#3<6F17$$!3HL$ek7%R=9F1$\"3\"Qc!\\ES#Q-\"F1 7$$!32+vo*=\"f-9F1$\"3_a5]W'efN*!#=7$$!3imm\"HD)y'Q\"F1$\"35gCdWPkA&)F C7$$!3K3-8-#QIP\"F1$\"3c%p@pl!ROyFC7$$!3!)\\PM^\")Gf8F1$\"3c[VZ)GZ`=(F C7$$!3]\"Hd05QbM\"F1$\"3_=7/s7molFC7$$!3?L3x\\!)yJ8F1$\"3gX2F>))[&)fFC 7$$!3y\\iS48'3I\"F1$\"3ez[j,U'>z%FC7$$!3em;/pX$*p7F1$\"3Y#zX[@FWv$FC7$ $!$D\"F*$\")D1kJF--%'COLOURG6&%$RGBG$\"\"&!\"\"$\"$l\"!\"$F]p-F$6$7-Fa o7$$!3gmm;EG!)Q7F1$\"3-Ghl\"[=$eGFC7$$!3hm;H$3rw?\"F1$\"3aPo#QKU>5#FC7 $$!3y\\i:/tow6F1$\"3GDb'p%y6z9FC7$$!3=L3-DNqX6F1$\"3W0R)yJiTx*!#>7$$!3 ()*\\ibfxp6\"F1$\"35Jqh0\\]KhFgq7$$!3cmT5m;D)3\"F1$\"3wYHGbEM'R$Fgq7$$ !3OL3-Iw]e5F1$\"3y#H)>()3a]9Fgq7$$!3%**\\PRfj(G5F1$\"3#)=zeH9D0M!#?7$$ !3qmTgJHQ85F1$\"3C))HLj>Jgs!#@7$$!0+++++++\"!#9$\"\"!FhsFfo-F$6$7OFcs7 $$!3UK$3FpA+)**FC$\"3Op)*R*p$=$f\"!#A7$$!3#*)*\\Ppg@E)*FC$\"3i(Rd!)pJr =\"F\\s7$$!3Ul;/Y%4Cn*FC$\"3q'*GUNA:`TF\\s7$$!39L$e*=Fyl$*FC$\"3ig$Q\" eK]3:Fgq7$$!3w**\\(=*f:f!*FC$\"3^?r?OgX:KFgq7$$!3=KL$eV\\$G%)FC$\"3'[L :mFC$\"3O5jlY-\"p:$FC7$$!3N****\\UR$R,'FC$\"3UU> wN1guSFC7$$!3yl;/'*yIkaFC$\"3it->nu!)>\\FC7$$!3CKL$eO\\2\"[FC$\"3#*Q#G 1)3&p!fFC7$$!31LLLj&*4dUFC$\"3#*[r3Y+'Qq'FC7$$!3c)*\\PCK28OFC$\"3I?$*e u]bfvFC7$$!3JMLL)y+I/$FC$\"3cArzKTxL#)FC7$$!3r)*\\Pu4a#=FC$\"3[$)45\")\\6Z$*FC7$$!3\"3L$3xT_+7FC$\"3w4V`l b#Qr*FC7$$!3W;$e9'G!>:*Fgq$\"3Y([%*p(o=L)*FC7$$!3wCL3_Rc)H'Fgq$\"3V:U^du$)*FC7$$\"31,]Pk&R; =\"FC$\"3_Plkj^pA(*FC7$$\"3oMLez#fFy\"FC$\"3Gm(p--bWP*FC7$$\"3l*****\\ wuPS#FC$\"3#G6#>)>gx())FC7$$\"3V***\\7E<8,$FC$\"3u;pQoGio#)FC7$$\"3q** \\ile9*f$FC$\"3#=yPB1Kqd(FC7$$\"3?***\\(3$H=D%FC$\"3MGf)p[07r'FC7$$\"3 'fmm;T%HQ[FC$\"3uX)zN1nh'eFC7$$\"3A++](3rWY&FC$\"3cwbaysb>\\FC7$$\"3YK $eRA!)=.'FC$\"3)[+Yi,\\q/%FC7$$\"3i++]#G3Al'FC$\"3BK8DPM&y5$FC7$$\"3tl ;HU'))eB(FC$\"3[5)yy6_(pAFC7$$\"3Y-]7)z-g%yFC$\"3QajJe?lx9FC7$$\"3Vlm; /4]U%)FC$\"3C;dJ&H%y]#)Fgq7$$\"3++]iS\"zp1*FC$\"3qec1+;![;$Fgq7$$\"3uo \"z>_-xO*FC$\"3InV*ew\"o*\\\"Fgq7$$\"3_PLL.fUo'*FC$\"3-)y:o6\\ID%F\\s7 $$\"3zO3F\\C>A)*FC$\"3E2_mT]BU7F\\s7$$\"31O$3_**ef(**FC$\"3!p'Q4&*\\K1 BFat7$$\"\"\"FhsFgsFfo-F$6$7-Fdal7$$\"3`$e9TbsH,\"F1$\"30\"[Ww=%4>oFbs 7$$\"3YL$3(3#\\$G5F1$\"3Wv/EN4\\1LF\\s7$$\"3G](o\\'y%)e5F1$\"3MzLe4b%z Y\"Fgq7$$\"33n\"H7_Y$*3\"F1$\"3k'e-x/(y%[$Fgq7$$\"3p$ek)=;P<6F1$\"3GrE >pf=whFgq7$$\"3I++];nRX6F1$\"3&zsL@Yf-t*Fgq7$$\"3_L3-Tm^x6F1$\"3uby#4x tT\\\"FC7$$\"3wm;allj47F1$\"3AzYPMMtX@FC7$$\"3,+v$*3]OQ7F1$\"37>\"RkcL n%GFC7$$\"$D\"F*FdoFfo-F$6$7/Fgdl7$$\"3ELLL_M4n7F1$\"3Op7))\\^hmOFC7$$ \"3k;z%\\'Rs(H\"F1$\"3GP:!)GpvzYFC7$$\"3.+DcxWNG8F1$\"3>([0n?%*\\%eFC7 $$\"3%*\\7.KJ,V8F1$\"3eraf.T3fkFC7$$\"33++]'yrwN\"F1$\"3l[1&f7)36rFC7$ $\"3A](o4WIBP\"F1$\"3P_RJmq--yFC7$$\"39+vV&4*)pQ\"F1$\"3-j2X)zKH`)FC7$ $\"35D\"y:#=u-9F1$\"3K*f@#*>NTO*FC7$$\"30](=xa%\\=9F1$\"39#3bEi+W-\"F1 7$$\"3+v$fQFZUV\"F1$\"3G>g0FpQ<6F17$$\"3'*************\\9F1F27$$\"$X\" F*F+Ffo-%)POLYGONSG6%717$FboFhsFaoFaoFcpFhpF]qFbqFhqF]rFbrFgrF]sFcsFcs 7$FdsFhs-%&STYLEG6#%,PATCHNOGRIDG-Fgo6&FioFeal$\"$%*)F_p$\"$#))F_p-Ffh l6%7=7$FgzFhsFjhlFcsFcsF\\tFbtFgtF\\uFauFfuF[vF`vFevFjvF_wFdwFiwF^xFcx FhxF]yFbyFgyF\\zFazFfzFfzF[ilF_il-Ffhl6%7 " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Example 3" }}{PARA 0 "" 0 "" {TEXT -1 63 "This example ill ustrates the region enclosed between the graph " }{XPPEDIT 18 0 "y = x ^3-x;" "6#/%\"yG,&*$%\"xG\"\"$\"\"\"F'!\"\"" }{TEXT -1 9 " and the " } {TEXT 276 1 "x" }{TEXT -1 24 " axis over the interval " }{XPPEDIT 18 0 "[-2, 2]" "6#7$,$\"\"#!\"\"F%" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 264 4 "Note" }{TEXT -1 67 ": The 1st colour is for the segment of the graph cut off above the " } {TEXT 274 1 "x" }{TEXT -1 62 " axis and the 2nd colour is for the segm ent cut off below the " }{TEXT 275 1 "x" }{TEXT -1 7 " axis. " }} {PARA 0 "" 0 "" {TEXT -1 113 "The colours for the shading of the regio ns is determined by lightening the colour for the corresponding segmen t. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "areaplot(x^3-x,x=[-2..2,-2.2..2.2],color=[gold,purple ]);" }}{PARA 13 "" 1 "" {GLPLOT2D 476 476 476 {PLOTDATA 2 "62-%'CURVES G6$7'7$$!#A!\"\"$!%[%)!\"$7$$!3;+++++++A!#<$!3'R+++++![%)F17$$!3$omm;_ #4/@F1$!3/@&\\b7d6@(F17$$!3QLLePRk??F1$!3=$yTU9\\'HiF17$$!\"#\"\"!$!\" 'FA-%'COLOURG6&%$RGBG$\"\"%F*FA$\"\"*F*-F$6$7/F>7$$!3#ommrF(zE>F1$!301 in8'HlA&F17$$!3\"pmm,aGB$=F1$!3FhlF%Q#e>VF17$$!3[LLe'z3$Q!)oiE pV^$F17$$!3smm\"*e/9^;F1$!3]=*o*ycI]GF17$$!3/++D%p#)3c\"F1$!3I@h.F8)>C #F17$$!3wmm\"\\)z`n9F1$!3mKYFE70$p\"F17$$!3/++DLE\\u8F1$!3`Sfp#3SAA\"F 17$$!3OLLL_Syy7F1$!30!pzW(*pR7)!#=7$$!3ymm;#)Q[%>\"F1$!3;Tx_,'ez4&Fap7 $$!3)******p&=e*4\"F1$!3)Hm1#3'3!*H#Fap7$$!32+++b,H/5F1$!3U?%>>D0cj)!# ?7$$!0+++++++\"!#9$FAFAFD-F$6$7/Fbq7$$!3y+++I%*eC\"*Fap$\"3ij\\j$pEw_ \"Fap7$$!3gom;\\Sn!H)Fap$\"3!*H')\\Vj0#f#Fap7$$!3GLLL.!o!*H(Fap$\"3mL^ ='z(Q5MFap7$$!3+LLL8w/fkFap$\"3[4,9;%yVw$Fap7$$!3'3++D?/>[&Fap$\"3t%)f Vn@_MQFap7$$!3vMLL8n'ph%Fap$\"3c+b*)okzKOFap7$$!3]****\\-K*zm$Fap$\"3G Wv#)4]\\uJFap7$$!39)***\\2gMkFFap$\"3m\"*)o$)\\0Jb#Fap7$$!3dKLLe\\[@=F ap$\"3SfDi%f^5w\"Fap7$$!3/JLLe=Wc&*!#>$\"3!pvSy4n\"p%*Fjt7$$!39'zmm;%z r@Faq$\"3A!=()H#Ryr@Faq7$FfqFfq-FE6&FG$\"$+)F-$\"$)\\F-$\"$'>F--F$6$7. Fbu7$$\"3/:LL3&*o$[*Fjt$!313v8dGR)R*Fjt7$$\"3%3++DWKGz\"Fap$!3T0;$ Fap7$$\"3)*)****\\:&*)oXFap$!3\"Q8y\\HZ^h$Fap7$$\"3)=++v.t2Y&Fap$!3%Re o]@oB$QFap7$$\"3)y****\\O^5X'Fap$!3sDss=xPmPFap7$$\"3pimm'[g3M(Fap$!3s VAb10+&Q$Fap7$$\"3[+++];#4H)Fap$!3q5QthLz\"f#Fap7$$\"3+ML$3F==:*Fap$!3 7M5&yqTm[\"Fap7$$\"\"\"FAFfqFD-F$6$7/F`y7$$\"3P+++n0I45F1$\"31t$pV,Wh) =Fjt7$$\"3CmmTm*ey4\"F1$\"3kv8V\"*>%QD#Fap7$$\"3E++v5!G/>\"F1$\"3ogO(R h*\\l\\Fap7$$\"3[mmmr6$4G\"F1$\"3.p^1P0,3#)Fap7$$\"3q***\\PfzcP\"F1$\" 3-ni[diyF7F17$$\"3'QLL`eLpY\"F1$\"3am!ei?_(*o\"F17$$\"3qLL$=(RDg:F1$\" 3%)pp/;1^$F17$$\"3.nm;^1JN=F1$\"3M%oUA&eoYVF17$$\"3#RLLth'[A>F1$\" 3!*zc17q$H=&F17$$\"\"#FA$\"\"'FAFcu-F$6$7'F]]l7$$\"3G++vzVV:?F1$\"3+f( )\\u6@rhF17$$\"3j++D[sR/@F1$\"3)4Z7mC+\\@(F17$$\"3;+++++++AF1$\"3'R+++ ++![%)F17$$\"#AF*$\"%[%)F-Fcu-%)POLYGONSG6%737$F?FAF>F>FOFTFYFhnF]oFbo FgoF\\pFbpFgpF\\qFbqFbq7$FcqFA-%&STYLEG6#%,PATCHNOGRIDG-FE6&%$HSVG$\") tS2u!\")$\"0++++++?#!#:$\"0+++++++\"Feq-Fj^l6%7,7$F_sFAF^_lFbqFbqFjqF_ rFdrFirF^sF^sF__l-FE6&Fe_l$\")MLL$)!\"*$\"0-_Ut*zn7F[`l$\"0++GS^[g*F[` l-Fj^l6%7-Fa`lF^sFcsFhsF]tFbtFgtF]uFbuFbu7$FfqFAF__lFb`l-Fj^l6%7-7$Fhw FAF^alFbuFbuF^vFcvFhvF]wFbwFgwFgwF__lFc_l-Fj^l6%7+FbalFgwF\\xFaxFfxF[y F`yF`y7$FayFAF__lFc_l-Fj^l6%737$F^]lFAFfalF`yF`yFfyF[zF`zFezFjzF_[lFd[ lFi[lF^\\lFc\\lFh\\lF]]lF]]lF__lFb`l-F$6&7$F]_lF>-%&COLORG6&FG$\"\"$F* FablFabl-%*THICKNESSG6#Fby-%*LINESTYLEGFebl-F$6&7$FjalF]]lF^blFcblFfbl -%+AXESLABELSG6$Q\"x6\"Q!F_cl-%%VIEWG6$;F(Fe^l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curv e 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curv e 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Example 4" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 63 "This example illustrates the region \+ enclosed between the graph " }{XPPEDIT 18 0 "y = x*(x-1)*(x-2)*(x-3)*( x-4);" "6#/%\"yG*,%\"xG\"\"\",&F&F'F'!\"\"F',&F&F'\"\"#F)F',&F&F'\"\"$ F)F',&F&F'\"\"%F)F'" }{TEXT -1 9 " and the " }{TEXT 284 1 "x" }{TEXT -1 24 " axis over the interval " }{XPPEDIT 18 0 "[0, 4]" "6#7$\"\"!\" \"%" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT 264 5 "Notes" }{TEXT -1 2 ": " }}{PARA 15 "" 0 "" {TEXT -1 12 "The option \"" }{TEXT 285 10 "zeros=true" }{TEXT -1 13 "\" causes the " }{TEXT 279 1 "x" }{TEXT -1 55 " coordinates of the points where the graph crosses the " }{TEXT 277 1 "x" }{TEXT -1 23 " axis to be displa yed. " }}{PARA 15 "" 0 "" {TEXT -1 12 "The option \"" }{TEXT 285 10 "a reas=true" }{TEXT -1 87 "\" causes the magnitude of the areas of the v arious regions cut off above and below the " }{TEXT 278 1 "x" }{TEXT -1 23 " axis to be displayed. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "areaplot(x*(x-1)*(x-2)*(x-3) *(x-4),x=[0..4,0..4.1],\n zeros=true,areas=true);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6(%,zeros~...~~G$\"\"!F%$\"\"\"F%$\"\"#F%$\"\"$F%$ \"\"%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%3signed~areas~...~~G$\"+++ +]A!\"*$!+nmmm\"*!#5$\"+nmmm\"*F)$!++++]AF&" }}{PARA 13 "" 1 "" {GLPLOT2D 506 412 412 {PLOTDATA 2 "66-%'CURVESG6$7%7$$\"\"!F)F(F'F'-%' COLOURG6&%$RGBGF(F($\"\"\"F)-F$6$7$F'F'F*-F$6$7?F'7$$\"3.LL3-$3UB#!#>$ \"3jP0m!4%R;^!#=7$$\"31mm;/mToWF9$\"3?4JGBDpc(*F<7$$\"3u)**\\i!\\i-nF9 $\"3'G@H@oUVR\"!#<7$$\"36KLL3K$o$*)F9$\"3GyYB'Qa)pqFFG7$$\"3_*\\(=AD^3 @F<$\"31))e*Gkhi9$FG7$$\"3%GL$eWEvXDF<$\"3#>fLQ&))*eS$FG7$$\"3)HLe9'=# ew#F<$\"3M%>SxJ8n\\$FG7$$\"35LLLy5*e)HF<$\"3!Hc,!R>)Hc$FG7$$\"3!H$3x'o Df4$F<$\"3S`e[S&*R(e$FG7$$\"3DL$3_Hgf?$F<$\"3K6EG]-E1OFG7$$\"3gLek.\\* fJ$F<$\"3ulxHK5v>OFG7$$\"3RLL37&HgU$F<$\"34)zVh*e0GOFG7$$\"3YvVBX6aNNF <$\"3Lt)Hxy^8j$FG7$$\"3)pT&QyF0XOF<$\"3\\D3+Pf')HOFG7$$\"3[ek`6WcaPF<$ \"3$Glp*R6xBOFG7$$\"3)**\\(oWg2kQF<$\"3kee!*ptB8OFG7$$\"3-$e*)4J*4$3%F <$\"3yOjW.)=&zNFG7$$\"3.m;HxD7-VF<$\"3\"**fUrG9+`$FG7$$\"3X**\\(oyZ#3Z F<$\"33U-Nr!*p+MFG7$$\"3)GLek*HP9^F<$\"3l*y8SS^!HKFG7$$\"3])*\\7e7TbfF <$\"3G3%zY,S#pFFG7$$\"3&>Le9B9_#oF<$\"3C4-chg\"[>#FG7$$\"31**\\iNxA#p( F<$\"3c3K2gMmu:FG7$$\"3ulm;%pdSe)F<$\"3(*f,*[S#\\N$*F<7$$\"3WKL32?ep$* F<$\"3yzE&3V%*y'RF<7$F.$!\"!F)-F+6&F-F.F(F(-F$6$74Fjt7$$\"3))***\\Kj*Q D5FG$!3!\\s-Hk[.\\\"F<7$$\"3y***\\P<%=96FG$!3K=&*GVx,LhF<7$$\"3y***\\n ;a(*>\"FG$!3')Q)4`%Q1o'*F<7$$\"3/Le9=*fuF\"FG$!3<5@B2z-,7FG7$$\"3v\\7G X(fOK\"FG$!3wvwdm8(**H\"FG7$$\"3WmmTs&f)p8FG$!3=.7[*zW)o8FG7$$\"3Sm;/' )o**39FG$!3(=Ql2/tRS\"FG7$$\"3cmmm*>M\"[9FG$!3Q^'f3H\"G=9FG7$$\"3G$e*[ *>gO\\\"FG$!3wO_5)Hk&49FG7$$\"3y*\\7$*>'=R:FG$!3Msz?enwu8FG7$$\"3/$eRK U%[z:FG$!3f#\\v=&fSB8FG7$$\"3Jmm;ZEy>;FG$!3'*>E,fX)RD\"FG7$$\"3%)*\\7V s4#3\"*e]/\"FG7$$\"3))*\\PH@8Cz\"FG$!3QsU/;p0gyF<7$$\"3gm;z >2F!)=FG$!398Fo#o+Oq%F<7$$\"3[m\"HsL^4'>FG$!3[3#[CNq*e:F<7$$\"\"#F)F(F *-F$6$74Fbz7$$\"3)HL3FGwz/#FG$\"3S]2tUC`8>F<7$$\"3)H$e9V2PQ@FG$\"3&*zc Qi9(GS&F<7$$\"3p*\\(o'Qfq@#FG$\"3/a;(G_ee<)F<7$$\"3KL$euFX?I#FG$\"3-oJ =*3:H2\"FG7$$\"3Q****\\=S%)*Q#FG$\"3])>1^>T@F\"FG7$$\"3;*\\i!))4zKCFG$ \"3Qj#*pk>-T8FG7$$\"3Q**\\idztvCFG$\"3+g6d@,'*)Q\"FG7$$\"3c\\(o*e8HsZjo7FG7$$\"3&emmrsMSt#FG$\"3=IF_HNsr6FG7$$\"3c***\\P: jD#GFG$\"3s9@M@A]S))F<7$$\"3qKe9mIy-HFG$\"3@8$z?F)*)=`F<7$$\"3k***\\#> Y[!*HFG$\"3#yR=F`INm&F97$$\"\"$F)F[uF]u-F$6$7=Fh_l7$$\"3ul\"zf%\\+tIFG $!3(y#=9Fq)ei%F<7$$\"3g*\\iXYi#fJFG$!3%[O%)**4!))e5FG7$$\"34mmTb\\fVKF G$!3AaapVk_n;FG7$$\"3F*\\7yD$)=L$FG$!3qzXC&RlXH#FG7$$\"3DLLL'Q:pT$FG$! 3guL`aheWGFG7$$\"3sK$3#>I(Q]$FG$!3[cqB^nE)H$FG7$$\"3c\\P44=*pa$FG$!3!> <*)*433jMFG7$$\"3Sm\"z*)f5,f$FG$!316h&Glhkd$FG7$$\"3(\\PfQW@*4OFG$!3n7 :-U@u3OFG7$$\"34$eR()GK(HOFG$!3&yU+`eAsi$FG7$$\"3:(oz6rP'ROFG$!3IH[!eK z4j$FG7$$\"3A\"z>O8V&\\OFG$!33FMQY@\"4j$FG7$$\"3G&*)fgb[%fOFG$!3v1dz#[ #*oi$FG7$$\"3y****\\yRNpOFG$!3i*Ry^')*y=OFG7$$\"3s;aQU%f?p$FG$!3-SU!pr #4%e$FG7$$\"3AL3F1\\w9PFG$!3s#GCz+QFG$!3'Hc9`w`!eIFG7$ $\"3'GLLV)zSTQFG$!3G>))zI*>?o#FG7$$\"3I;H#=>8Z)QFG$!3yW%3Ms9U:#FG7$$\" 3u*\\7$*R=!GRFG$!3Sq,b5!y7[\"FG7$$\"3#*\\i!RqU([RFG$!3+p)y7KaM5\"FG7$$ \"3o****\\3qYpRFG$!3O=4M2AmroF<7$$\"3U\\P488>!*RFG$!3NcWLd!4jI#F<7$$\" \"%F)F(F*-F$6$7$F[hlF[hlF*-F$6$7+F[hl7$$\"3;*\\(o " 0 "" {MPLTEXT 1 0 131 "f := x -> x*(x-1)*(x-2)*(x-3)*(x-4);\nInt(f(x),x=0..1),Int(f(x),x =1..2),Int(f(x),x=2..3),Int(f(x),x=3..4);\nop(value([%]));\nevalf(%); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&a rrowGF(*,9$\"\"\",&F-F.F.!\"\"F.,&F-F.\"\"#F0F.,&F-F.\"\"$F0F.,&F-F.\" \"%F0F.F(F(F(" }}{PARA 12 "" 1 "" {XPPMATH 20 "6&-%$IntG6$*,%\"xG\"\" \",&F'F(F(!\"\"F(,&F'F(\"\"#F*F(,&F'F(\"\"$F*F(,&F'F(\"\"%F*F(/F';\"\" !F(-F$6$F&/F';F(F,-F$6$F&/F';F,F.-F$6$F&/F';F.F0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&#\"\"*\"\"%#!#6\"#7#\"#6F(#!\"*F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&$\"++++]A!\"*$!+nmmm\"*!#5$\"+nmmm\"*F($!++++]AF%" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Example 5" }}{PARA 0 "" 0 "" {TEXT -1 53 "This example illustrates the region under the graph \+ " }{XPPEDIT 18 0 "y = x*exp(-x);" "6#/%\"yG*&%\"xG\"\"\"-%$expG6#,$F& !\"\"F'" }{TEXT -1 7 " from " }{XPPEDIT 18 0 "x=1" "6#/%\"xG\"\"\"" } {TEXT -1 4 " to " }{XPPEDIT 18 0 "x = 3;" "6#/%\"xG\"\"$" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 264 4 "Not e" }{TEXT -1 172 ": The options \"ord_color\" and ord_style\" can be u sed to control the colour and linestyle of the vertical left-hand and \+ right-hand boundary lines of the region illustrated. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "areaplot( x*exp(-x),x=[1..3,0..4],color=tan,ord_style=2,ord_color=blue,areas=tru e);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%3signed~areas~...~~G$\"+*31hO& !#5" }}{PARA 13 "" 1 "" {GLPLOT2D 463 236 236 {PLOTDATA 2 "6+-%'CURVES G6$7%7$$\"\"!F)F(F'F'-%'COLOURG6&%$RGBG$\"$f)!\"$$\"$w&F0$\"$R%F0-F$6$ 79F'7$$\"3emmm;arz@!#>$\"3$>j31*yrK@F;7$$\"39LLLL3VfVF;$\"3gXx#eQnM<%F ;7$$\"3s******\\i9RlF;$\"3xKvnCHADhF;7$$\"3Hmmmm;')=()F;$\"3QNWwNM(3*z F;7$$\"3-++]7z>^7!#=$\"3OLqK>g//6FP7$$\"3RLLLe'40j\"FP$\"3'yOv)Qg>&Q\" FP7$$\"3/++](Q&3d?FP$\"3OM@^U@hu;FP7$$\"3mmmm;6m$[#FP$\"3_'p-))>Su$>FP 7$$\"3jmmmmW18HFP$\"3y0qsbT*o<#FP7$$\"3fmmm;yYULFP$\"39'o15:'z#R#FP7$$ \"3/++](GI)pPFP$\"3_R&pW2Jee#FP7$$\"3%HLL$eF>(>%FP$\"3ioHOIk_eFFP7$$\" 3Q*****\\Z7Mf%FP$\"3ehJ*o,d;!HFP7$$\"3Qmmm\">K'*)\\FP$\"3h2r;4U]HIFP7$ $\"3P*****\\Kd,\"eFP$\"3GPXO'*\\z\\KFP7$$\"3-mmm\"fX(emFP$\"3lk#>)RIU@ MFP7$$\"3.*****\\U7Y](FP$\"3Up:Z1KHVNFP7$$\"3'QLLLV!pu$)FP$\"3O\"*)3r5 /Yi$FP7$$\"3K+++DI(yv)FP$\"3#4m,^Y^zk$FP7$$\"3xmmm;c0T\"*FP$\"3w%GRw)3 UkOFP7$$\"3+LLLe%GCd*FP$\"3cOEXkULvOFP7$$\"\"\"F)$\"0U9F]s7$$\"3#*******H,Q+5!#<$\"3-]5*f9%zyOFP7$$\"3&*******RXpV5Fis$\"3 _Yj\"=D$QvOFP7$$\"3)*******\\*3q3\"Fis$\"3oZ9+V6llOFP7$$\"3)*******p= \\q6Fis$\"3v65)*yL.JOFP7$$\"3mmm;fBIY7Fis$\"3;jVM3P%Re$FP7$$\"3GLLLj$[ kL\"Fis$\"3%p%=.hH)=^$FP7$$\"3?LLL`Q\"GT\"Fis$\"3td(*RszfRMFP7$$\"3!** ***\\s]k,:Fis$\"3/VPjob6XLFP7$$\"39LLL`dF!e\"Fis$\"3?'*4])3xSD$FP7$$\" 33++]sgam;Fis$\"3/K,-e&y![JFP7$$\"3/++]Fis$\"3\"R,lk0ET#GFP7$$\"3 immmTc-)*>Fis$\"3U4rVmwP4FFP7$$\"3Mmm;f`@'3#Fis$\"3]CWsRV;!f#FP7$$\"3y ****\\nZ)H;#Fis$\"3C<$HS]Iq[#FP7$$\"3YmmmJy*eC#Fis$\"3uzneF$*)oP#FP7$$ \"3')******R^bJBFis$\"3y()4p#*)y\\E#FP7$$\"3f*****\\5a`T#Fis$\"3II8]vM xd@FP7$$\"3o****\\7RV'\\#Fis$\"3;BK[1%=l0#FP7$$\"3k*****\\@fke#Fis$\"3 )Qr`[KXs%>FP7$$\"3/LLL`4NnEFis$\"37_;v(p*4_=FP7$$\"3#*******\\,s`FFis$ \"35eUrIw&Qv\"FP7$$\"3[mm;zM)>$GFis$\"3U.rX$pAzm\"FP7$$\"3$*******pfa< HFis$\"3'G+!)pP1ud\"FP7$$\"3#HLLeg`!)*HFis$\"3;7PI*4^b\\\"FP7$$\"\"$F) $\"0#f.^?h$\\\"FbsF*-F$6$70Fi[l7$$\"3w****\\#G2A3$Fis$\"3y[BdciV89FP7$ $\"3;LLL$)G[kJFis$\"3MB$*zl-bO8FP7$$\"3#)****\\7yh]KFis$\"3+$zW_&Gif7F P7$$\"3xmmm')fdLLFis$\"3!)p))fU6$*)=\"FP7$$\"3bmmm,FT=MFis$\"3Sgh]IC-? 6FP7$$\"3FLL$e#pa-NFis$\"3khm5Er)\\0\"FP7$$\"3!*******Rv&)zNFis$\"3G!G TCeC0)**F;7$$\"3ILLLGUYoOFis$\"3Y:btThJg$*F;7$$\"3_mmm1^rZPFis$\"34@gX ;F%R$))F;7$$\"34++]sI@KQFis$\"3uN(*4!z&>,$)F;7$$\"34++]2%)38RFis$\"3.& =/,BVy\"yF;7$$\"\"%F)$\"3'Gn$\\bbDEtF;7$Fi_l$\"0o$\\bbDEt!#;F*-%)POLYG ONSG6%7B7$F^sF)F]sF]sFfsF\\tFatFftF[uF`uFeuFjuF_vFdvFivF^wFcwFhwF]xFbx FgxF\\yFayFfyF[zF`zFezFjzF_[lFd[lFi[lFi[l7$Fj[lF)-%&STYLEG6#%,PATCHNOG RIDG-F+6&%$HSVG$\")!3lV&!\"*$\"0yZC)QvV')F``l$\"0++7++!=(*Fbs-F$6&7$Fe `lF]s-F+6&F-F(F(F^s-%*THICKNESSG6#F_s-%*LINESTYLEG6#\"\"#-F$6&7$Ff`lFi [lFhalFjalF]bl-%+AXESLABELSG6$Q\"x6\"Q!Fhbl-%%VIEWG6$;F(Fi_l%(DEFAULTG " 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "C urve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "Int( x*exp(-x),x=1..3);\nvalue(%);\nevalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*&%\"xG\"\"\"-%$expG6#,$F'!\"\"F(/F';F(\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"%\"\"\"-%$expG6#!\"$F&!\"\"*&\"\"#F& -F(6#F+F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+*31hO&!#5" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Example 6" }}{PARA 0 "" 0 "" {TEXT -1 75 "This example illustrates the area of the region encl osed between the graph " }{XPPEDIT 18 0 "y = sin(1/x);" "6#/%\"yG-%$si nG6#*&\"\"\"F)%\"xG!\"\"" }{TEXT -1 9 " and the " }{TEXT 280 1 "x" } {TEXT -1 43 " axis over the interval [0.00964, 0.0199]. " }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "areap lot(sin(1/x),x=0.00964..0.0199,color=[blue,gold]);" }}{PARA 13 "" 1 " " {GLPLOT2D 603 324 324 {PLOTDATA 2 "6in-%'CURVESG6$7%7$$\"$k*!\"&$!0u =YwxU='!#;7$$\"3F************R'*!#?$!3a![3YwxU='!#>F'-%'COLOURG6&%$RGB G$\"$+)!\"$$\"$)\\F;$\"$'>F;-F$6$7$F'7$$\"0a\"yETvX'*!#<$\"0[;Bn#po))F47$$\"3-\\(=-&[&zm*F1$\" 3]F-ck0BeB!#=7$$\"3)Q7G`FK>o*F1$\"3s,6Ae'Gxx$FW7$$\"3w)\\P/q4fp*F1$\"3 Pr9\\BzW4^FW7$$\"3itoaDr))4(*F1$\"3l\\o!yL$yCjFW7$$\"3][il]X'Qs*F1$\"3 )p=/(>M4)R(FW7$$\"3PBcwv>%yt*F1$\"3\\\">P'*e-sI)FW7$$\"3C)*\\(3S>=v*F1 $\"3QHR5$)\\\"Q.*FW7$$\"37tV)f#ozl(*F1$\"31N/AFM$Qc*FW7$$\"3)zu$4^Uxz( *F1$\"3'z^XLfzv))*FW7$$\"3IO%[O'Hw'y*F1$\"3oQ<`seJq**FW7$$\"3'G7.in^Pz *F1$\"3'*oN`IO\"*****FW7$$\"3U4yv)QS2!)*F1$\"3]&o\"=PFWw**FW7$$\"3t(\\ 785Hx!)*F1$\"3c!yAw\"QD+**FW7$$\"3ZZ7`^RoN)*F1$\"3]YH&ovd[3*FW7$$\"3'* )**\\ #e#FW7$$\"3S6yDIcD&)**F1$!33@w6NG')RPFW7$$\"3k#f3JJ8=5F4$!37mhBY;XxtFW7 $$\"39cE0d'*\\>5F4$!38HGuh'[lU'FW7$$\"3y'H%[lt'3-\"F4$!3C0*Q&)Qhw2+$FW7$ $\"3r=#z2\\q\\-\"F4$!3h\"*Hd`CHNQj-\"F4$!3NXY$o86$QWF47 $$\"0%QY%31o-\"F-$!0=^0ewg4\"FIF5-F$6$75Fc[l7$$\"3***\\Uw!fqF5F4$\"3F& 4%HP9u;&)F47$$\"3]PM8#o#3H5F4$\"3$3'[B?d(y8#FW7$$\"3,vVic%f/.\"F4$\"31 s&[B@DYQ$FW7$$\"3_7`6Ji$=.\"F4$\"3]y->)>@8d%FW7$$\"3.]ig0I@L5F4$\"3SF \"3K1R'ycFW7$$\"30D\")eal'f.\"F4$\"3;6;)H^&)fe(FW7$$\"32++d.,sQ5F4$\"3 )G/IW3)4))*)FW7$$\"34v=b_OZT5F4$\"3E%)*R#Q7A-)*FW7$$\"36]P`,sAW5F4$\"3 !ooqBROa)**FW7$$\"39Dc^]2)p/\"F4$\"3E.<-Q`&f`*FW7$$\"3)**\\(\\*HM(\\5F 4$\"3e3k#[2_<\\)FW7$$\"3i=59<2FFW7$$\"3ilA&f\"fKf5F4$\"3Xy.y0F\"H^\"FW7$$\"3/vV(o9'pg5F4$ \"3GeB[\"eSA*HF47$$\"0(f%R&H.h5F-$!0%)\\,$zQ:(*!#GF[u-F$6$7k0:)=#R%FW7$$\"3q@\\[, tan5F4$!3A\\=U&\\:$RaFW7$$\"35JqSKv\"*o5F4$!3Ztse8oL0kFW7$$\"3]S\"HLw( Gq5F4$!3#p$QJ(=/qF(FW7$$\"3!*\\7D%*zlr5F4$!3Z$[_C])eU!)FW7$$\"3%\\P%=` ()>u5F4$!3=k$fn?0&[\"*FW7$$\"3)**\\<@^Rn2\"F4$!3Ncn%)*[`&3)*FW7$$\"3= \"y]=qut2\"F4$!3]'=BfPH/!**FW7$$\"3SiSe\"*)4!y5F4$!3#pp$GQSdi**FW7$$\" 3yVtJ\"3X'y5F4$!39%>3cu1\\***FW7$$\"3+D10r-Gz5F4$!3#>))*>piV(***FW7$$ \"3g(=<0l]03\"F4$!3zRJbTNc8**FW7$$\"3/]P)*H5#=3\"F4$!3B)G=cx!y7(*FW7$$ \"31vo\"*)yhV3\"F4$!3Q(>Th$3^u*)FW7$$\"35++&ya-p3\"F4$!3!y![*z%))>ByFW 7$$\"3'\\7$y1LW*3\"F4$!3L@WLCc_4\"F4$!3sC`D8/,JXFW 7$$\"39D12q%*H$4\"F4$!3h%*[\")['4L_$FW7$$\"37+]Uu[h%4\"F4$!3%Hg8a*fWvC FW7$$\"35v$z(y-$f4\"F4$!3:G$\\U;=.S\"FW7$$\"33]P8$oXs4\"F4$!36ASlPI)*4 JF47$$\"0\\&=(H?w4\"F-$\"0:\"emT:RSFIF5-F$6$79Fail7$$\"31D\")[(3h&)4\" F4$\"3s-y@!*fF%z(F47$$\"3/+D%=\\w)*4\"F4$\"3+zwE!3;!e=FW7$$\"3-vo>'*=> ,6F4$\"3[PnGIv67HFW7$$\"3+]7b+t]-6F4$\"3y0LP:3_HRFW7$$\"3'****f#4\"Q^5 \"F4$\"3=#e%Gu#*Q3eFW7$$\"3#*\\(oz\"*ox5\"F4$\"3RR9p.Ej5uFW7$$\"3))*\\ xms*R56F4$\"3g%\\X86)*om)FW7$$\"3,]iQN0.86F4$\"3O*o-%*y^^_*FW7$$\"33]7 XG4R96F4$\"3D>+azN)\\c=**FW7$$\"33]i x$*G>@6F4$\"3gm_')eN'=T*FW7$$\"30]i!*zO\"R7\"F4$\"3Ye1)**[O%p%)FW7$$\" 3,]i.mWjE6F4$\"3p'y\\^B459(FW7$$\"3)*\\i;__NH6F4$\"3[yIrs[!G\\&FW7$$\" 3()\\7BXcrI6F4$\"3yg*eYkj'f#FW7$$\"3\"*\\iUCozM6F4$\"3Q%*GD^4ki:FW7$$ \"3QPMpaG:O6F4$\"3w+H1k*e3<&F47$$\"0(\\3A5#o8\"F-$!0KZ,apn5#FIF[u-F$6$ 79Fb`m7$$\"3%[ig\\))3v8\"F4$!3[$[MX*yz;`F47$$\"3[7yA:\\')Q6F4$!3wjO))[ *H@d\"FW7$$\"3&***\\\\X4AS6F4$!3+D\\Kzd'Hf#FW7$$\"31v$Hg+LH9\"F4$!3'Q( G'zF[C`%FW7$$\"3+]Pcm]kX6F4$!3%)eRNX#o'oiFW7$$\"3%\\7)4FrN[6F4$!3&o_b6 e?2t(FW7$$\"3))*\\Kw=p5:\"F4$!3ul\\2mT\"4'))FW7$$\"3![(o;[7y`6F4$!3/\" y[q@knh*FW7$$\"3#*\\7q3L\\c6F4$!3I5\"HaumA(**FW7$$\"3Sf$3D:))y:\"F4$!3 =hp9H')f&***FW7$$\"3qoaJ'*HGf6F4$!3*\\(\\Pf*44\"**FW7$$\"3+yD7Syng6F4$ !3<)oaS!z))>(*FW7$$\"3I(oHRos?;\"F4$!3WCH$epS`U*FW7$$\"331RarB'[;\"F4$ !3;*zeP$e?U&)FW7$$\"3'[7e\"f?ln6F4$!35Ms()zRG/tFW7$$\"3kVBxYyiiu6F4$!3_t4L:q& \\0$FW7$$\"3?\"y+?7@g<\"F4$!3YAMtE*e&z?FW7$$\"3o!*y!e'fTx6F4$!3Emq&zA+R'FW7$$\"3i7.Y,m4\">\"F4$\"3[Jr$*G[KAwFW 7$$\"33v$H)fPb$>\"F4$\"3c\")3xN9*>i)FW7$$\"3cP%)>=4,'>\"F4$\"3W_S([&\\ Bi$*FW7$$\"3-+vcw!o%)>\"F4$\"3jnfG_zXC)*FW7$$\"3#pHa6if\"*>\"F4$\"3dgf )>t;G!**FW7$$\"3!Q4Td;^)*>\"F4$\"3UY96:**>e**FW7$$\"3r!*yK5Fa+7F4$\"3O Pn>/!f0***FW7$$\"3g(o9\\DM7?\"F4$\"3_q8:F*)*)****FW7$$\"3S\"G)3Wth-7F4 $\"3O9]@``!)\\**FW7$$\"3-v=EL/+/7F4$\"3dbN]bu+4)*FW7$$\"3Wi!4;hmn?\"F4 $\"39b'=sFW7$$\"30D1lY^1:7F4$\"3!z<)y#[1)*z&FW7$$\"3Z7y*\\KJy@\"F 4$\"3OxG\"oWyZ=%FW7$$\"31+]M.vf?7F4$\"3ugEq#Qd@V#FW7$$\"3-]i))R]PB7F4$ \"3s$3SAa/Q'fF47$$\"0e9IzoUA\"F-$!0`'zsG+?CFealF[u-F$6$76Fd^n7$$\"3)** \\Fkd_hA\"F4$!3EGJDV0h^7FW7$$\"3%*\\(oH6I*G7F4$!3-l!>V`T)[IFW7$$\"32++ ^\\wqJ7F4$!3^v2s3nXNZFW7$$\"3?]70'=&[M7F4$!3I%3T*\\UjciFW7$$\"3;+DfAFE P7F4$!39hHZysDkvFW7$$\"37]P8f-/S7F4$!3_I(ea#eH=')FW7$$\"33+]n&z\\()FW7$$\"33++TAy()e7F4$!39U HxaTS3yFW7$$\"33+D`$\\a:E\"F4$!3E*)fK%e9)\\mFW7$$\"33+]lk6Bk7F4$!3Fp*f N=E)3`FW7$$\"3I1RYQ=mm7F4$!3'zOy$3ORmRFW7$$\"3]7GF7D4p7F4$!32b.MSdPQDF W7$$\"3))=<3'=B:F\"F4$!3EFW7$$\"3oP%3v?:)y7F4$\"3Y?)\\IO?yN$FW7$$\"3)QM<8)eC\"G\"F4$ \"3y$Q%HkL=8ZFW7$$\"35]i7bln$G\"F4$\"3AjD9%\\+0'fFW7$$\"3wV[Qhoc'G\"F4 $\"3CKs[t*3vE(FW7$$\"3gPMknrX*G\"F4$\"3I)4\"RBE=[$)FW7$$\"3WJ?!RZZBH\" F4$\"3q]LGr%**H<*FW7$$\"37D1;!yP_H\"F4$\"3q#*4\"4:Y2s*FW7$$\"3%>#**GLH o'H\"F4$\"3)zEk3G\")H\"F4$\"3/BuOQ\\*)y**FW7$$\"3i :&[&RKd*H\"F4$\"3u>B!f?hy***FW7$$\"3X7yn#R=5I\"F4$\"3_R\"o\"zvqV**FW7$ $\"371k$*)p3RI\"F4$\"3HU/*e%e2?'*FW7$$\"3(***\\>0!*z18F4$\"3)f0Ab0;6-* FW7$$\"3*\\7=PZZ#48F4$\"3a&efsI)[8$)FW7$$\"3$)\\7CUfp68F4$\"3\"pye8pi% RuFW7$$\"3&[Pk2TWTJ\"F4$\"3>'=*GCRa=kFW7$$\"3()*\\(GzGf;8F4$\"3;\"3c&G :$GF&FW7$$\"3)[i5yMT!>8F4$\"3phkL(p4l-%FW7$$\"3!*\\PL;)*[@8F4$\"39icy) 47`q#FW7$$\"3#\\(o&[GQRK\"F4$\"3hFMrvL(fL\"FW7$$\"0YKC>\"HE8F-$\"08!)e l*oFiFealF[u-F$6$7:F\\\\o7$$\"3%****zLv'QE8F4$!3!**)pX#o=@V&F17$$\"3=J XM/\\BH8F4$!3[W$3Z59?m\"FW7$$\"3Ui!4`0$3K8F4$!3M*oY(y\"*))>KFW7$$\"3m$ fti?J\\L\"F4$!3e*G\">6:d)o%FW7$$\"3!\\7QsNzxL\"F4$!3szxN*)*))*><#)FW7$$\"3i= <85QKY8F4$!3'R;%\\&o6#4!*FW7$$\"3/]i4h><\\8F4$!3MGhs(>(Qw&*FW7$$\"3))o /IdIp^8F4$!3GDDy4.'=))*FW7$$\"3a(o/N:9UN\"F4$!3ee(*[9!)p)***FW7$$\"3)o z1;quaN\"F4$!3;v$pAY.i)**FW7$$\"3A1*3(\\_tc8F4$!3-A[8U!)yE**FW7$$\"3c: 5\"yz&*zN\"F4$!3+BxT'3\"*4#)*FW7$$\"3)[78fMc#f8F4$!3i**Gy?Vcp'*FW7$$\" 3Si:KQ&)Hk8F4$!3vm!*)QZ_'H')FW7$$\"3#****H2tS$p8F4$!3/Oc0`'[+(pFW7$$\" 3C\"GQGx1@P\"F4$!3e_Y%*=h\"G%eFW7$$\"3cil%\\\"G([P\"F4$!3ovm6_IW%f%FW7 $$\"3)Q%[0d)QwP\"F4$!3u6J'*y%RID$FW7$$\"3/DJ;**[S!Q\"F4$!3%>Rpt'R\"F4$\"3b$zdPJT09'FW7$$\"3mPM>Y3P*R\" F4$\"3a$z;j'RDXrFW7$$\"31+DRsZ+-9F4$\"3[c1^r3Q7$)H!H9F4$\"3c\\mzJ!fZf(FW7$$\"3>\"y!*o0y@YW\"F4$\"35Om.!zY02\"FW7$$\"0B J'oW\"F-$\"0ycX=#Qv[FealF[u-F$6$7:F][p7$$\"3')=<\"z#\\9Z9F4$!3Y(HXh*o' eM\"F47$$\"3_i:)plo'\\9F4$!37n\"HRl&fL8FW7$$\"3?190'Q#>_9F4$!3[*o@o*4G 4DFW7$$\"3/]77:hra9F4$!3m+dmPX2XOFW7$$\"3=Jq'yHQuX\"F4$!3&)Q+%o@0u![FW 7$$\"3]7Gh![g,Y\"F4$!35;'fBvBn)eFW7$$\"3%QfeLm#)GY\"F4$!3'fU;I5\"RmoFW 7$$\"3)\\P/h%[gl9F4$!3iX%=sK!pJxFW7$$\"3YPff6#\\5Z\"F4$!3W3*Gum?52*FW7 $$\"3#**\\(3xN\\w9F4$!3m\\#RFS'eJ)*FW7$$\"3yrh\\ot!zZ\"F4$!36%GIPt\"GH **FW7$$\"3mV[!*f6Kz9F4$!3mQrBdTC&)**FW7$$\"3_:NJ^\\t![\"F4$!3MY.Pp'y%* ***FW7$$\"3Q(=AFu[@[\"F4$!3G'eW))Rk@(**FW7$$\"37J&RbKw\\[\"F4$!3cAWyhw X%z*FW7$$\"3-voN3R!y[\"F4$!3#>2Y^!p!pX*FW7$$\"3ki:*R2fM\\\"F4$!3_ODH:u $QL)FW7$$\"33]iiRU6*\\\"F4$!3ea:Q[D8)o'FW7$$\"30Dc$z2PS]\"F4$!3ZGz$>z` !>\\FW7$$\"3,+]C;*f*3:F4$!38n[2=x.IHFW7$$\"3[(o*RN8U6:F4$!3[=W$RH3J)=F W7$$\"3'\\PaXv#)Q^\"F4$!3M.v$zWQw<)F47$$\"0'*zFOhd^\"F-$\"0\\5^:x+e\"F IF5-F$6$7;Fcbp7$$\"3Wi!4PR%H:F4 $\"3Y#**QNhMOc&FW7$$\"3`7Ge$*fvM:F4$\"3O(e<_r$f(G(FW7$$\"32+D#Qzs+a\"F 4$\"3x1Xc6OPJ')FW7$$\"3/v$>(obcX:F4$\"3G>IX.s`d&*FW7$$\"3+]ihV$e5b\"F4 $\"3e,*Qsn()e(**FW7$$\"3yo/MP:V_:F4$\"3?eqeWvA****FW7$$\"3c(ok5t/Qb\"F 4$\"3aND]P75!***FW7$$\"3=1*)yCzZ;y:F4$\"3!*y#GOnO-3&FW7$$\"3A+D$zKQNe \"F4$\"3!Q:4d[)RDJFW7$$\"3#)o/E\\z8'e\"F4$\"3!Gpo2'fFF@FW7$$\"3wP%)eqv t)e\"F4$\"3#>RqJ3_(46FW7$$\"3o1k\">>P8f\"F4$\"3%p&3^'Rz)z$)F17$$\"0&*= 4V\\:f\"F-$\"0MB8Z2BN\"FIF[u-F$6$7;F^jp7$$\"3GvVC8o$Rf\"F4$!3Q)4WL(e+( R*F47$$\"3)QMsXVOlf\"F4$!3#3:[Gdk+&>FW7$$\"3Y7.!f0O\"*f\"F4$!3(*HxQ-8# p$HFW7$$\"31\"GGsnN%G(\\ x+[FW7$$\"3Si!z5<3,h\"F4$!3/.t;#)*[bi'FW7$$\"3:v=gV5)eh\"F4$!3)Hra\"GG Y6\")FW7$$\"3b(oCh\"Rl@;F4$!3Kj`D6yX$>*FW7$$\"3'**\\Z')yEui\"F4$!3XvM3 SO=G)*FW7$$\"3QcwK%eB(G;F4$!3?FuJo&*o1**FW7$$\"3X7y+!Q?+j\"F4$!3[C#pgi >9'**FW7$$\"3`ozovrJJ;F4$!3i!zg7ecB***FW7$$\"3&\\7o8(RhK;F4$!3],c,T,a* ***FW7$$\"3P\"G[qw5Rj\"F4$!3e5W)oAmI)**FW7$$\"3WP%GFc2_j\"F4$!3A2[YCh3 V**FW7$$\"3_$f3%eV]O;F4$!3gC)e;^0)z)*FW7$$\"3%*\\()3a6!yj\"F4$!3'H.F+P $[$z*FW7$$\"3#\\P4oL))Hk\"F4$!3U#3:sbaZA*FW7$$\"3#****H&>b<[;F4$!3Q!4R N(G.@$)FW7$$\"3)*\\iEWRr`;F4$!3!eN$p%4*eIqFW7$$\"3/+D+pBDf;F4$!35.$)>% f:`n\"F-$!0=dx4#p%G\"FIF5-F$6$78Fiaq7$$\"3!G\"yXayMv;F4$ \"3]fW!G=sP;\"F17$$\"33D1W!\\m.o\"F4$\"3oPB6%H=Zy\"FW7$$\"3OPMUE^Q&o\" F4$\"3oYz\"y(QG\"\\$FW7$$\"3)*\\iSiPS!p\"F4$\"37gsi\"))R%z]FW7$$\"3_P4 8d/*ep\"F4$\"3I4l4bAFDmFW7$$\"30Dc&=:x8q\"F4$\"3mfR30&G;#zFW7$$\"3e7.e YQ'oq\"F4$\"3;%4IFI+p#*)FW7$$\"36+]IT0N7Qys\"F4$\"3=c%Qr$)zXq*FW7$$\"38]i*)\\2+LCn2<7FIF[u-F$6$74Fehq7$$\"3Qi:nORTq&HP/BFW7$$\"3M7y!>E87y\"F4$!3[]U: %f@+'RFW7$$\"3)[iSUmOny\"F4$!3o'o<;)p='[&FW7$$\"3UPMdm+E#z\"F4$!3p6K$e *4sRoFW7$$\"3'*\\i!*oMy(z\"F4$!3=H*oNY)*Q)zFW7$$\"30DJuaGU3=F4$!33sMWm Pr&\\*FW7$$\"38++eSA1>=F4$!3gL7;S\"**)****FW7$$\"3&*\\(y#\\D%*H=F4$!3w `bkp&\\gX*FW7$$\"36+v(z&G#3%=F4$!3`h];0L]MzFW7$$\"3w(=-^'z@Y=F4$!3S7/& HA+E(oFW7$$\"3/voAsIh^=F4$!3s\\p>\"G0bk&FW7$$\"3qi:Nz\"3q&=F4$!3Us_&)G BP'G%FW7$$\"3M]iZ'G.C'=F4$!3G5,cm!\\1$GFW7$$\"3u(o4'H3On=F4$!3I#[00\"R PR9FW7$$\"3;DJus$=B(=F4$!3=Zr)[-l[k#F17$$\"0x)>&46C(=F-$\"0e^P\\'Q0&)F ealF5-F$6$79F]^r7$$\"3cil(e\"fFx=F4$\"3/kjQI/fz8FW7$$\"3)****4!fMB#)=F 4$\"3y\\z:%G(3^FFW7$$\"3'[P**GO:z)=F4$\"3Q[3uTRrYUFW7$$\"35]()ymsf$*=F 4$\"30hfoLm1EcFW7$$\"3OD\"y1F4 $\"3JpN[;)[2\"zFW7$$\"3K]Pr**\\7:>F4$\"3)RPBu@.!)G*FW7$$\"3R++'[#*)GD> F4$\"3QlQ/y@*f%**FW7$$\"3]J&*)39)*z#>F4$\"3MkfXG\")>&***FW7$$\"3ii!>pN 22$>F4$\"3=UfgK\"p7***FW7$$\"3t$f[Hd;M$>F4$\"3'p+EkNrY$**FW7$$\"3>D\"y *)yDh$>F4$\"33n86&4Vh#)*FW7$$\"3x(=P5AW:%>F4$\"39J)o*GDbd%*FW7$$\"3+]i 4`E'p%>F4$\"3!\\*fcNxY'*))FW7$$\"33DJ&Ry[@&>F4$\"3%z+2116E>)FW7$$\"39+ +\"[\"\\Ld>F4$\"3&yV(4XzOTtFW7$$\"3?vomX5_i>F4$\"3k&Qf@QG1O'FW7$$\"3G] P_wrqn>F4$\"3#**ftLpv,F&FW7$$\"3u7GR#Q!Gt>F4$\"3=\"=4.zJ.+%FW7$$\"3?v= E)e`)y>F4$\"3iw0s\\%4gl#FW7$$\"3mP48%zEW)>F4$\"358\\\"p(pil7FW7$$\"0p[ ')yO%*)>F-$\"0_neq(f%=)!#HF[u-F$6$7%F^er7$$\"37++++++!*>F4$!354:f<'pDU \"F47$$\"$*>!\"%$!0e%f<'pDU\"F-F5-F$6$7$F\\frF\\frF5-%)POLYGONSG6%7(7$ F(F^uF'F'FCFC7$FDF^u-%&STYLEG6#%,PATCHNOGRIDG-F66&%$HSVG$\")MLL$)!\"*$ \"0-_Ut*zn7!#:$\"0++GS^[g*Fggr-Fffr6%737$F`qF^uFjfrFCFCFMFRFXFgnF\\oFa oFfoF[pF`pFepFjpF_qF_qF[gr-F66&Fagr$\")nmmm!\")$\"0+++++++#Fggr$\"0+++ ++++\"!#9-Fffr6%71F]hrF_qFdqFiqF^rFcrFhrF]sFbsFgsF\\tFatFftFft7$FgtF^u F[grF^hr-Fffr6%717$FbxF^uF[irFftFftFduFiuF^vFcvFhvF]wFbwFgwF\\xFaxFaxF [grF_gr-Fffr6%70F_irFaxFfxF[yF`yFeyFjyF_zFdzFizF^[lFc[lFc[l7$Fd[lF^uF[ grF_gr-Fffr6%707$Fd^lF^uFcirFc[lFc[lF[\\lF`\\lFe\\lFj\\lF_]lFd]lFi]lF^ ^lFc^lFc^lF[grF^hr-Fffr6%7/FgirFc^lFh^lF]_lFb_lFg_lF\\`lFa`lFf`lF[alF` alF`al7$FaalF^uF[grF^hr-Fffr6%757$F[flF^uF[jrF`alF`alFialF^blFcblFhblF ]clFbclFgclF\\dlFadlFfdlF[elF`elFeelFjelFjelF[grF_gr-Fffr6%71F_jrFjelF _flFdflFiflF^glFcglFhglF]hlFbhlFghlF\\ilFailFail7$FbilF^uF[grF_gr-Fffr 6%727$F\\]mF^uFcjrFailFailFiilF^jlFcjlFhjlF][mFb[mFg[mF\\\\mFa\\mFf\\m F[]mF[]mF[grF^hr-Fffr6%71FgjrF[]mF`]mFe]mFj]mF_^mFd^mFi^mF^_mFc_mFh_mF ]`mFb`mFb`m7$Fc`mF^uF[grF^hr-Fffr6%717$FhcmF^uF[[sFb`mFb`mFj`mF_amFdam FiamF^bmFcbmFhbmF]cmFbcmFgcmFgcmF[grF_gr-Fffr6%72F_[sFgcmF\\dmFadmFfdm F[emF`emFeemFjemF_fmFdfmFifmF^gmFcgmFcgm7$FdgmF^uF[grF_gr-Fffr6%737$Fc [nF^uFc[sFcgmFcgmF[hmF`hmFehmFjhmF_imFdimFiimF^jmFcjmFhjmF][nFb[nFb[nF [grF^hr-Fffr6%70Fg[sFb[nFg[nF\\\\nFa\\nFf\\nF[]nF`]nFe]nFj]nF_^nFd^nFd ^n7$Fe^nF^uF[grF^hr-Fffr6%707$FeanF^uF[\\sFd^nFd^nF\\_nFa_nFf_nF[`nF`` nFe`nFj`nF_anFdanFdanF[grF_gr-Fffr6%70F_\\sFdanFianF^bnFcbnFhbnF]cnFbc nFgcnF\\dnFadnFfdnFfdn7$FgdnF^uF[grF_gr-Fffr6%737$FfhnF^uFc\\sFfdnFfdn F^enFcenFhenF]fnFbfnFgfnF\\gnFagnFfgnF[hnF`hnFehnFehnF[grF^hr-Fffr6%71 Fg\\sFehnFjhnF_inFdinFiinF^jnFcjnFhjnF][oFb[oFg[oF\\\\oF\\\\o7$F]\\oF^ uF[grF^hr-Fffr6%727$Fg_oF^uF[]sF\\\\oF\\\\oFd\\oFi\\oF^]oFc]oFh]oF]^oF b^oFg^oF\\_oFa_oFf_oFf_oF[grF_gr-Fffr6%72F_]sFf_oF[`oF``oFe`oFj`oF_aoF daoFiaoF^boFcboFhboF]coFbcoFbco7$FccoF^uF[grF_gr-Fffr6%727$F]goF^uFc]s FbcoFbcoFjcoF_doFddoFidoF^eoFceoFheoF]foFbfoFgfoF\\goF\\goF[grF^hr-Fff r6%73Fg]sF\\goFagoFfgoF[hoF`hoFehoFjhoF_ioFdioFiioF^joFcjoFhjoF][pF][p 7$F^[pF^uF[grF^hr-Fffr6%747$Fb_pF^uF[^sF][pF][pFe[pFj[pF_\\pFd\\pFi\\p F^]pFc]pFh]pF]^pFb^pFg^pF\\_pFa_pFa_pF[grF_gr-Fffr6%70F_^sFa_pFf_pF[`p F``pFe`pFj`pF_apFdapFiapF^bpFcbpFcbp7$FdbpF^uF[grF_gr-Fffr6%727$F^fpF^ uFc^sFcbpFcbpF[cpF`cpFecpFjcpF_dpFddpFidpF^epFcepFhepF]fpF]fpF[grF^hr- Fffr6%73Fg^sF]fpFbfpFgfpF\\gpFagpFfgpF[hpF`hpFehpFjhpF_ipFdipFiipF^jpF ^jp7$F_jpF^uF[grF^hr-Fffr6%747$Fc^qF^uF[_sF^jpF^jpFfjpF[[qF`[qFe[qFj[q F_\\qFd\\qFi\\qF^]qFc]qFh]qF]^qFb^qFb^qF[grF_gr-Fffr6%71F__sFb^qFg^qF \\_qFa_qFf_qF[`qF``qFe`qFj`qF_aqFdaqFiaqFiaq7$FjaqF^uF[grF_gr-Fffr6%72 7$FdeqF^uFc_sFiaqFiaqFabqFfbqF[cqF`cqFecqFjcqF_dqFddqFidqF^eqFceqFceqF [grF^hr-Fffr6%70Fg_sFceqFheqF]fqFbfqFgfqF\\gqFagqFfgqF[hqF`hqFehqFehq7 $FfhqF^uF[grF^hr-Fffr6%7/7$Fa[rF^uF[`sFehqFehqF]iqFbiqFgiqF\\jqFajqFfj qF[[rF`[rF`[rF[grF_gr-Fffr6%7/F_`sF`[rFe[rFj[rF_\\rFd\\rFi\\rF^]rFc]rF h]rF]^rF]^r7$F^^rF^uF[grF_gr-Fffr6%707$F^arF^uFc`sF]^rF]^rFe^rFj^rF__r Fd_rFi_rF^`rFc`rFh`rF]arF]arF[grF^hr-Fffr6%73Fg`sF]arFbarFgarF\\brFabr FfbrF[crF`crFecrFjcrF_drFddrFidrF^erF^er7$F_erF^uF[grF^hr-Fffr6%7)7$F] frF^uF[asF^erF^erFgerF\\frF\\frF[grF_gr-F$6&7$FifrF'-%&COLORG6&F8$\"\" $!\"\"FfasFfas-%*THICKNESSG6#F`u-%*LINESTYLEGF[bs-F$6&7$F_asF\\frFcasF iasF\\bs-%+AXESLABELSG6$Q\"x6\"Q!Febs-%%VIEWG6$;F(F]fr%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2 " "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9 " "Curve 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" "Curve 15" "C urve 16" "Curve 17" "Curve 18" "Curve 19" "Curve 20" "Curve 21" "Curve 22" "Curve 23" "Curve 24" "Curve 25" "Curve 26" "Curve 27" "Curve 28 " "Curve 29" "Curve 30" "Curve 31" "Curve 32" "Curve 33" "Curve 34" "C urve 35" "Curve 36" "Curve 37" "Curve 38" "Curve 39" "Curve 40" "Curve 41" "Curve 42" "Curve 43" "Curve 44" "Curve 45" "Curve 46" "Curve 47 " "Curve 48" "Curve 49" "Curve 50" "Curve 51" "Curve 52" "Curve 53" "C urve 54" "Curve 55" "Curve 56" "Curve 57" "Curve 58" "Curve 59" }}}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Example 7" }}{PARA 0 "" 0 "" {TEXT -1 75 "This example illustrates the area of the region encl osed between the graph " }{XPPEDIT 18 0 "y = exp(x)-4+x^2;" "6#/%\"yG, (-%$expG6#%\"xG\"\"\"\"\"%!\"\"*$F)\"\"#F*" }{TEXT -1 9 " and the " } {TEXT 289 1 "x" }{TEXT -1 24 " axis over the interval " }{XPPEDIT 18 0 "[-3, 2]" "6#7$,$\"\"$!\"\"\"\"#" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "areaplot(ex p(x)-4+x^2,x=-3..2,zeros=true,areas=true,\n color=[darken(ora nge),dark_green],ord_color=black,ord_style=2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%,zeros~...~~G$!+(fNY'>!\"*$\"+,k+e5F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&%3signed~areas~...~~G$\"+&pm7U#!\"*$!+wtoFkF&$\"+z jN7IF&" }}{PARA 13 "" 1 "" {GLPLOT2D 476 476 476 {PLOTDATA 2 "6/-%'CUR VESG6$7%7$$!\"$\"\"!$\"0'yOoqy\\]!#97$F($\"3]kyOoqy\\]!#,b,LF17$$!3wmm\"H_\">#e#F1$\"3xU!4k=@Lu#F17$$!3ML$3_!4N vCF1$\"3LrC7mb\\6AF17$$!3'omTg(fHwBF1$\"3,G1\\)ew'R1#F 1$\"3Ed\"RMbtty$Fco7$$!0'))[(fNY'>F-$!\"#F-F2-F$6$7AFio7$$!3;LL$epjJ&> F1$!3U]X8K1pKV!#>7$$!3amm\"z/ot&=F1$!3ZaaZ;/,TRFco7$$!3))****\\P[_\\F17$$!33U.\\UJF17$$!35kmT5!3B#RFco$!3#*[7(*>ogqJF17$$!3C***\\iS!p iHFco$!37[^m4tjoJF17$$!3lim;/rFE>Fco$!391k%ye0\"QJF17$$!3Q&******\\2cb )Ffp$!3_$4jL\\yY2$F17$$\"3t9++DJE>>Ffp$!33XG9\\OD!)HF17$$\"3t-+D1RU07F co$!3#3C$)3(4OdGF17$$\"3+++](=S2L#Fco$!3Q-\"*4z:?$o#F17$$\"3:jmm;p)=M$ Fco$!3ay5(QB6:\\#F17$$\"3O-++v=]@WFco$!39+bj*y`%[AF17$$\"3/JLe*[$z*R&F co$!3e\")pZx3X#*>F17$$\"3#e++]iC$pkFco$!3=v)o+b/=n\"F17$$\"3ukm\"H2qcZ (Fco$!3L!3Pz$zGH8F17$$\"3i.+DJ5fF&)Fco$!3i,`=&>3pE*Fco7$$\"3akmmTg.c&* Fco$!3O//+p7#e'[Fco7$$\"0k!4,k+e5F-$\"\"#F--F36&%$RGBG$F*F*$\"%FR!\"%F [z-F$6$70Fcy7$$\"3w**\\ilAFj5F1$\"3KkyMyU$zj#Ffp7$$\"3yLLL$)*pp;\"F1$ \"3?aYmZmjSdFco7$$\"3)RL$3xe,t7F1$\"3!**y'[*Gx@>\"F17$$\"3Cn;HdO=y8F1$ \"3e$yl**eyq'=F17$$\"3a+++D>#[Z\"F1$\"3//a\\!=d`a#F17$$\"3SnmT&G!e&e\" F1$\"3q7!4LU)='R$F17$$\"3#RLLL)Qk%o\"F1$\"3q#)HCYfbGUF17$$\"37+]iSjE!z \"F1$\"3'z)zs$[,h>&F17$$\"3L+++DM\"3%=F1$\"3uq7(>^7d*4Dc?'F17$$\"3G+voa-oX>F1$\"3Y@>(ydiSy'F17$$FgyF*$\"3S]1 $*)4c!*Q(F17$Fj]l$\"0lI*)4c!*Q(F-F2-F$6$7$F]^lF]^lF2-%)POLYGONSG6%717$ F(F*F'F'FAFFFKFPFUFZFinF^oFdoFioFio7$FjoF*-%&STYLEG6#%,PATCHNOGRIDG-F3 6&F5F6$\"0+++gmmm#F=F9-Fd^l6%777$F^uF*Fh^lFioFioFapFgpF\\qFaqFfqF[rF`r FerFjrF_sFdsFisF^tFctFhtF]uF]uFi^l-F36&F5$\")LLLL!\")$\"0+++++Y@$F=F9- Fd^l6%74Fd_lF]uFbuFguF\\vFavFfvF[wF`wFewFjwF_xFdxFixF^yFcyFcy7$FdyF*Fi ^lFe_l-Fd^l6%747$Fj]lF*F_`lFcyFcyFbzFgzF\\[lFa[lFf[lF[\\lF`\\lFe\\lFj \\lF_]lFd]lFi]lF]^lF]^lFi^lF]_l-F$6&7$Fg^lF'-F36&FjyF*F*F*-%*THICKNESS G6#\"\"\"-%*LINESTYLEG6#Fgy-F$6&7$Fc`lF]^lFg`lFi`lF]al-%+AXESLABELSG6$ Q\"x6\"Q!Fgal-%%VIEWG6$;F(Fj]l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve \+ 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 62 " The zeros and signed areas can also be calculated as follows. " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "f := x -> exp(x)-4+x^2;\na := fsolve(f(x),x=-2);\nb := fsolve(f(x ),x=1);\nInt(f(x),x=-3..a),-Int(f(x),x=a..b),Int(f(x),x=b..2);\nevalf( %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG %&arrowGF(,(-%$expG6#9$\"\"\"\"\"%!\"\"*$)F0\"\"#F1F1F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG$!+(fNY'>!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG$\"+,k+e5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6% -%$IntG6$,(-%$expG6#%\"xG\"\"\"\"\"%!\"\"*$)F*\"\"#F+F+/F*;!\"$$!+(fNY '>!\"*-F$6$F&/F*;F4$\"+,k+e5F6-F$6$F&/F*;F;F0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%$\"+&pm7U#!\"*$!+wtoFkF%$\"+zjN7IF%" }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Example 8" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "Let " }{XPPEDIT 18 0 "f(x) " "6#-%\"fG6#%\"xG" }{TEXT -1 51 " be the piecewise function defined o n the interval " }{XPPEDIT 18 0 "[-2,2]" "6#7$,$\"\"#!\"\"F%" }{TEXT -1 4 " by " }}{PARA 257 "" 0 "" {TEXT -1 2 " " }{XPPEDIT 18 0 "f(x) = PIECEWISE([1-sqrt(-2*x-x^2), -2 <= x and x < 0],[1-sqrt(2*x-x^2), 0 < = x and x <= 2]);" "6#/-%\"fG6#%\"xG-%*PIECEWISEG6$7$,&\"\"\"F--%%sqrt G6#,&*&\"\"#F-F'F-!\"\"*$F'F3F4F431,$F3F4F'2F'\"\"!7$,&F-F--F/6#,&*&F3 F-F'F-F-*$F'F3F4F431F:F'1F'F3" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 75 "This example illustrates \+ the area of the region enclosed between the graph " }{XPPEDIT 18 0 "y \+ = f(x);" "6#/%\"yG-%\"fG6#%\"xG" }{TEXT -1 9 " and the " }{TEXT 281 1 "x" }{TEXT -1 24 " axis over the interval " }{XPPEDIT 18 0 "[-2, 2];" "6#7$,$\"\"#!\"\"F%" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 164 "f := x -> piecewise(x<0,1- sqrt(-2*x-x^2),1-sqrt(2*x-x^2)):\n'f(x)'=f(x);\nareaplot(f(x),x=-2..2, areas=true,color=brown,\n shading=lighten(neon_blue,.7)) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"fG6#%\"xG-%*PIECEWISEG6$7$,& \"\"\"F-*$,&*&\"\"#F-F'F-!\"\"*$)F'F1F-F2#F-F1F22F'\"\"!7$,&F-F-*$,&*& F1F-F'F-F-F3F2F5F2%*otherwiseG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&%3si gned~areas~...~~G$\"+m$=g9#!#5$\"+Kn.#H%F&F$" }}{PARA 13 "" 1 "" {GLPLOT2D 683 314 314 {PLOTDATA 2 "6/-%'CURVESG6$7%7$$!\"#\"\"!$\"\"\" F*F'F'-%'COLOURG6&%$RGBG$\"\"&!\"\"$\"$l\"!\"$F4-F$6$7!#<$\"3K\\$yU.5BE*!#=7$$!3SL$e9r]X*>F=$\"3!zU()*z1Yd*)F@7$$!35+v=ng #=*>F=$\"3u/vrDx-C()F@7$$!3#om;HU,\"*)>F=$\"3qZDw!>Uw_)F@7$$!3A+]PM@l$ )>F=$\"3GuI@.\"4#*>)F@7$$!3SLL$e%G?y>F=$\"3W!oo%pQ[BzF@7$$!3)****\\(oU In>F=$\"3yjh`oG\"QY(F@7$$!3ymmm\"p0k&>F=$\"33@ZT^kezqF@7$$!3&*****\\P& 3Y$>F=$\"3()3yI5%>KW'F@7$$!3MLLL$Q6G\">F=$\"3Z.!G.(e=;fF@7$$!31++v3-)[ (=F=$\"3e3$f:N1m:&F@7$$!3bmm;M!\\p$=F=$\"3'\\o0Jj\">FXF@7$$!3#)***\\7Y \"H%z\"F=$\"33>Kd%3JY#RF@7$$!3MLLL))Qj^/MF@7$$!3Z$e&=F@7$$!3OLL$3yO5]\"F=$\"3i,2^*4SdM\"F@7$$!3&*****\\nU)*=9 F=$\"3G1)Reo]1?*!#>7$$!3SLL$3WDTL\"F=$\"3QopA;&Qru&Fer7$$!35++]d(Q&\\7 F=$\"374csJ)=N;$Fer7$$!3gmmmc4`i6F=$\"3PV3m7blH8Fer7$$!3KLLLQW*e3\"F=$ \"3ELijwlv&p$!#?7$$!3qmm;arvU5F=$\"374@mhF0X\"*!#@7$$!0(************** !#:$\"\"#FdtF--F$6$7OFat7$$!3w++++()>'***F@$\"31@&\\?6T\\A(!#D7$$!3_++ ++Y0j&*F@$\"3;u.\"3&[i]&*F`t7$$!3E++++0\"*H\"*F@$\"331\"*z/,Z#z$Fjs7$$ !35++++83&H)F@$\"3q\"ft%4<4k9Fer7$$!3\\LLL3k(p`(F@$\"3E\"RIs/'p!3$Fer7 $$!3Anmmmj^NmF@$\"3B&\\I()Q3)HeFer7$$!3)zmmmYh=(eF@$\"3vpM/u$e%=*)Fer7 $$!3+,++v#\\N)\\F@$\"3A&*pQ[YE\\8F@7$$!3commmCC(>%F@$\"3Qpv*>I*zb=F@7$ $!39*****\\FRXL$F@$\"3AS1cB;OXDF@7$$!3V******\\0zBHF@$\"3*H8owcxS$HF@7 $$!3t*****\\#=/8DF@$\"31bh&f+j3P$F@7$$!3%HLL3ioW3#F@$\"3iPrwkl**))QF@7 $$!3=mmm;a*el\"F@$\"3-oT*Htk&)[%F@7$$!3_mm;H9Li7F@$\"3&oh%))*y\\l8&F@7 $$!3komm;Wn(o)Fer$\"3Q9m6wR;BfF@7$$!3sNL$3x9^c'Fer$\"3%>7(H!>.kV'F@7$$ !3$G++]7bDW%Fer$\"3[C\")**>:]_qF@7$$!3QOL3-`F\"Q$Fer$\"3%f#*[ao&e@uF@7 $$!3$*pm;za**>BFer$\"3cjZhkhYeyF@7$$!3[.+Dccre7Fer$\"3:A@'p=f$=%)F@7$$ !3IqLLL$eV(>Fjs$\"3g'RVF4A>P*F@7$$\"3O$fmTNc$\\!*Fjs$\"3KP?FYCtd')F@7$ $\"3qbm;/rI2?Fer$\"3C;7j))*Hk+)F@7$$\"31_m\"Hdy'4JFer$\"36I\"yG%)*fDvF @7$$\"3V[mmT+07UFer$\"37hMa`bHGrF@7$$\"3:Tm;zHz;kFer$\"3M(e?I#y`vkF@7$ $\"3)Qjmm\"f`@')Fer$\"3()H-Ho*4!QfF@7$$\"3mILLL1+Y7F@$\"3'39N.I1g;&F@7 $$\"3%z****\\nZ)H;F@$\"3*)*G!yGT?GXF@7$$\"3DJL$e*HTW?F@$\"3>%)**>F[BTR F@7$$\"3ckmm;$y*eCF@$\"3]Srfh(GCV$F@7$$\"3cJLLe[E()GF@$\"3goDo3l%3(HF@ 7$$\"3f)******R^bJ$F@$\"3q5[\\\")HQiDF@7$$\"3'e*****\\5a`TF@$\"3)fLKE4 9r)=F@7$$\"3'o****\\7RV'\\F@$\"3CO?92HVg8F@7$$\"3Y'*****\\@fkeF@$\"3g< w)eZS9&*)Fer7$$\"3_ILLL&4Nn'F@$\"35#z1UeI\\p&Fer7$$\"3A*******\\,s`(F@ $\"3e!f5l/C,3$Fer7$$\"3%[mm;zM)>$)F@$\"3iTa9T?e@9Fer7$$\"3M*******pfa< *F@$\"3e&\\],*480MFjs7$$\"3Ckm;zy*zd*F@$\"3QtR%=Nd#3*)F`t7$$\"39HLLeg` !)**F@$\"3G4h4?pA%*=!#B7$$\"0)**************Fdt$F*F*F--F$6$7=Fcbl7$$\" 3Lmm;W/8S5F=$\"3#*oq'\\I2b0)F`t7$$\"3w****\\#G2A3\"F=$\"39Z)=Q!pu%Q$Fj s7$$\"3;LLL$)G[k6F=$\"3]Kfh]i+i8Fer7$$\"3#)****\\7yh]7F=$\"3u9p(HA*Q\" >$Fer7$$\"3xmmm')fdL8F=$\"3%=(>$fWyws&Fer7$$\"3bmmm,FT=9F=$\"3MqnS\"=) Hu\"*Fer7$$\"3FLL$e#pa-:F=$\"3+nu.m1]a8F@7$$\"3!*******Rv&)z:F=$\"3#zX UG9@G&=F@7$$\"3ILLLGUYo;F=$\"3A#*H4cqbiDF@7$$\"3\"*****\\n'*33F=$\"32ntFQNQAfF@7$$\"31+]i0j\"[$>F=$\"3q6[V)p$ o[kF@7$$\"3/++v.Uac>F=$\"3i;F=$\"33t$o(H$yx Y(F@7$$\"3-+](=5s#y>F=$\"3b@j!y0\\n#zF@7$$\"39]iSwSq$)>F=$\"3lpb7k'[?? )F@7$$\"3-+v$40O\"*)>F=$\"3mq'4aJq*H&)F@7$$\"3%[7.#Q?&=*>F=$\"3'\\z?[5 [gs)F@7$$\"3!*\\(oa-oX*>F=$\"3M_0l3P6f*)F@7$$\"3%\\PMF,%G(*>F=$\"3)*)) Qo+8[j#*F@7$$FftF*F+FbjlF--F$6$7$FbjlFbjlF--%)POLYGONSG6%7@7$F(F*F'F'F :FAFFFKFPFUFZFinF^oFcoFhoF]pFbpFgpF\\qFaqFfqF[rF`rFfrF[sF`sFesF[tFatFa t7$FbtF*-%&STYLEG6#%,PATCHNOGRIDG-F.6&%$HSVG$\")nmmm!\")$\"0+++++S4#Fd t$\"0+++++++\"!#9-Fhjl6%7=7$Fe[lF*F\\[mFatFatFjtF`uFeuFjuF_vFdvFivF^wF cwFhwF]xFbxFgxF\\yFayFfyF[zF`zFezFjzF_[lFd[lFd[lF][mFa[m-Fhjl6%7 " 0 "" {MPLTEXT 1 0 45 "evalf(4-Pi,11);\nevalf(1-Pi/4);\nevalf(2-Pi/2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+kM2%e)!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+l$=g9#!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*tO ?H%!\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}} }{SECT 1 {PARA 4 "" 0 "" {TEXT 0 8 "areaplot" }{TEXT -1 55 ": examples of animated construction of area functions " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Example 1" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 40 "Thi s example illustrates the graphs of " }{XPPEDIT 18 0 "f(x) = 6*sin(x) ;" "6#/-%\"fG6#%\"xG*&\"\"'\"\"\"-%$sinG6#F'F*" }{TEXT -1 41 " and it s antiderivative on the interval " }{XPPEDIT 18 0 "[0, 6*Pi];" "6#7$\" \"!*&\"\"'\"\"\"%#PiGF'" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 264 5 "Notes" }{TEXT -1 2 ": " }}{PARA 15 " " 0 "" {TEXT -1 12 "The option \"" }{TEXT 285 17 "areafunction=true" } {TEXT -1 111 "\" causes an animation to be constructed which shows the \"area function\" being drawn.\n( Redraw with the option \"" }{TEXT 285 17 "areafunction=true" }{TEXT -1 14 "\" instead of \"" }{TEXT 285 18 "areafunction=false" }{TEXT -1 28 "\" to obtain the animation. )" } }{PARA 15 "" 0 "" {TEXT -1 74 "The number of frames for the animation \+ can be specified using the option \"" }{TEXT 285 8 "frames=n" }{TEXT -1 2 "\"." }}{PARA 15 "" 0 "" {TEXT -1 107 "The colour of the area fun ction graph can be specified as the 3rd colour in the list for the col our option." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 142 "areaplot(6*sin(x),x=0..6*Pi,color=[brown$2,coral], shading=lighten([purple,cyan],.8),areafunc tion=false,frames=40);" }}{PARA 13 "" 1 "" {GLPLOT2D 607 332 332 {PLOTDATA 2 "66-%'CURVESG6$7%7$$\"\"!F)F(F'F'-%'COLOURG6&%$RGBG$\"\"&! \"\"$\"$l\"!\"$F1-F$6$7$F'F'F*-F$6$7>F'7$$\"3w5O!4pmr-\"!#=$\"3MyD(*=& o@:'F=7$$\"3_@s!=QLV0#F=$\"3Ra`qJ%[RA\"!#<7$$\"3;K3rs+]\"3$F=$\"3&4iZ9 $yx>=FE7$$\"30VWhjnm3TF=$\"3!>7;2:CkR#FE7$$\"3M/Sma78'*eF=$\"3-CR)*oqB OLFE7$$\"31lNrXdf$o(F=$\"3!zTO:uR(pTFE7$$\"3aHS(4^'y$p*F=$\"37sWINe?Z \\FE7$$\"3S\\MiFxRq6FE$\"3;KB0%>Ma_&FE7$$\"3o.#\\$3Ndr7FE$\"3WDXjS_RLd FE7$$\"3ud\\2*G\\FP\"FE$\"3oqNs8ir#)eFE7$$\"3*[$yVzrLB9FE$\"3(QO,l^&)[ $fFE7$$\"3#=r+)p]#RZ\"FE$\"3k?O(o))p=(fFE7$$\"3&*)ej,'H^C:FE$\"3c(eRqp uN*fFE7$$\"33mk_]35v:FE$\"3Kj@J8W%***fFE7$$\"3Q!)pZ0$[ai\"FE$\"3YCyv8< /\"*fFE7$$\"3m%\\F/w&zv;FE$\"3#3@YEtbp'fFE7$$\"3(*3!y`@Vhs\"FE$\"3([<@ =^Zx#fFE7$$\"3EB&G.n!\\wFE$\"3G'pDG@v'4bFE7$$\"3U_%yFj%fk@FE$\"3IvWX k(GH(\\FE7$$\"3)[KEax38N#FE$\"3Qpwk+$=LE%FE7$$\"3*f(HBb/kWDFE$\"3+UkBt jusLFE7$$\"3cF'R]8szt#FE$\"3]6p(p+.lN#FE7$$\"3g#\\f[.;z$HFE$\"3RV/Mmyi 87FE7$$\"34e$zY$*fy8$FE$\"3/hjRXhiRA!#>7$$\"0z*e`EfTJ!#9$\"0(*HgexI%>! #GF*-F$6$7=Fit7$$\"3dKn(=hirL$FE$!37Z6DeR&f;\"FE7$$\"3^2T2*Glk`$FE$!3( oAi?xV\"3BFE7$$\"32DY)**es9u$FE$!3iAoLf-E(Q$FE7$$\"3iU^*3*)zk%RFE$!3Se _&z)[^CVFE7$$\"3qE\\7L/0FTFE$!3#3U^^b]6+&FE7$$\"3y5ZNv4i2VFE$!3\\h)4op i^^&FE7$$\"3Lv3n`vw'fFE7$$ \"3IpBphgEn[FE$!3?!4hq*H=GfFE7$$\"3rp@y[YH=\\FE$!3[\"\\E?JdK(eFE7$$\"3 _q<'H#=N?]FE$!3$\\s]\\F=xr&FE7$$\"3Kr89(**3C7&FE$!3+p;giqn-bFE7$$\"3c \"[aK*46>`FE$!3#R2V!y(G\"H\\FE7$$\"3o#fn$*)H\"e^&FE$!3#Gbz%y$ya;%FE7$$ \"3'oHEiCPWp&FE$!3L+zd+=#>L$FE7$$\"3'>+&3.:1teFE$!37fVX4sL#R#FE7$$\"3e 5:CiAEzfFE$!3g3[v0Xf&z\"FE7$$\"3?>!)R@IY&3'FE$!3#G'zzM!>'y6FE7$$\"3!y_ a0yj;>'FE$!3')yJl!zGO[&F=7$$\"0fzrI&=$G'F\\u$\"01Sz#[%Q6#F_uF*-F$6$7=F `]l7$$\"3WO5rRX'yH'FE$\"3Ve%pV@Bs!))Fht7$$\"3#p=vk['zxkFE$\"3i))[27/Jg 6FE7$$\"3]O$RKVGxl'FE$\"3sDF9(>%3&>#FE7$$\"3m=)zB1Kq'oFE$\"3ZzKEZ_U2LF E7$$\"3%3I?:pNj2(FE$\"3e0(y9w-aF%FE7$$\"3=\\ZWo[ghsFE$\"37+>)='fpx\\FE 7$$\"3](>p`/uoW(FE$\"3*pMDAc>'4bFE7$$\"3)*=Zqq)3&[vFE$\"3)Qqo.FHAs&FE7 $$\"3eR-/'pV,l(FE$\"3s`o]'G\"yveFE7$$\"3K+!3(36'4q(FE$\"3#pd]%=6*)HfFE 7$$\"3=gdP@&y]zFE$\"3U#e&>56DsfFE7$$\"3M6U5HRe)*zFE$\"3s*Rbxvzt$fFE7 $$\"3!z=NK7up/)FE$\"3OBT(\\33'))eFE7$$\"3DRr\\6XvV\")FE$\"3/-v%=y_)\\d FE7$$\"3P#4f(**[`S#)FE$\"3#erE/$QGdbFE7$$\"3%=#H?k_\\U%)FE$\"3o)oMYJ+1 *\\FE7$$\"3b\\nkGcXW')FE$\"3Hp*)e(>^5A%FE7$$\"3QM(3%)G=*H))FE$\"3mL\"R 6AbBO$FE7$$\"3+@2<[4Q:!*FE$\"3Gx>]fuL)Q#FE7$$\"3dt!f=[Fa@*FE$\"3KuzFDw %pC\"FE7$$\"3\"zUZb,uaT*FE$\"3me&4af'G#e&Fht7$$\"0Qp2'zxC%*F\\u$!0'45> Cn2&*FE$!3mj9mKi* FE$!3Q!)>hFX7$=\"FE7$$\"3Nj'>_?irs*FE$!3?2Zf@Fy'y\"FE7$$\"3UUPWo#e5$)* FE$!3[$f*zD5%>,5!#;$!3T#\\0(oK,CLFE7$$\"3@'[F#eDG>5Fe gl$!3K?&[kn$RoTFE7$$\"3\"zL@()[=)Q5Fegl$!3lw8;/X%o#\\FE7$$\"3g*=:#>WNe 5Fegl$!3ujYF6$ey\\&FE7$$\"39^86$oX%o5Fegl$!3nA6t8D&>r&FE7$$\"3m7v+Zp`y 5Fegl$!3=V7'y=Hz'eFE7$$\"3M$fb*yDe$3\"Fegl$!3-XG*f#RgBfFE7$$\"3?uO!4@G ')3\"Fegl$!3C^IQ98?kfFE7$$\"3/b<&G%Qn$4\"Fegl$!3y3Y\\?!='*)fFE7$$\"3sN )*zu%>()4\"Fegl$!3Q#e#=^$*y**fFE7$$\"3T`)*GTcl.6Fegl$!3S(*)y85i\\*fFE7 $$\"3#4()zx!=f36Fegl$!3A50t[1`vfFE7$$\"3V)))pU(z_86Fegl$!3@CizHBaTfFE7 $$\"3&f!*f29k%=6Fegl$!3?2\\\"G%*zI*eFE7$$\"3(4%*RPZO$G6Fegl$!3gBC&*p,C `dFE7$$\"3=w*>n!)3#Q6Fegl$!3ce%[L9ttb&FE7$$\"3S_\")G'y7t:\"Fegl$!3JPw^ o]!o-&FE7$$\"3WGj&ew;k<\"Fegl$!3#>EN%y\\L8VFE7$$\"3wOu-y%Gw>\"Fegl$!3K LbPjSfQLFE7$$\"31X&)>!>S)=7Fegl$!3z2h'H#**>9AFE7$$\"38(H8q&)**yB\"Fegl $!3zG=i#\\lw6\"FE7$$\"0#fVhqjc7!#8$\"0,)el*oFi\"!#FF*-F$6$7>F\\^m7$$\" 3O\\!GQ_fpD\"Fegl$\"3*p)ew**4xM>Fht7$$\"3'ej#4bY8n7Fegl$\"3!eM9OF%*pG' F=7$$\"3=AsN'y4tF\"Fegl$\"3g*f8jiZ:B\"FE7$$\"3[3=i<\\[(G\"Fegl$\"3,\"* >*Q?c;#=FE7$$\"3![R'))[+m(H\"Fegl$\"3)H*[(3%3#HR#FE7$$\"3Z]:Q6/5;8Fegl $\"3a*z:**>J7O$FE7$$\"3)fqwQxSXL\"Fegl$\"3BL5)>Vnb@%FE7$$\"3gB>#3'4qa8 Fegl$\"3OE8U4)=^)\\FE7$$\"3ATrwZ6'[P\"Fegl$\"3O;*4VuVFb&FE7$$\"3g7[;Id M%Q\"Fegl$\"3Ez&)GH!fIu&FE7$$\"3!Q[iDJIQR\"Fegl$\"3e&))e7-]<)eFE7$$\"3 S>8w.Ed)R\"Fegl$\"3bk0z`$G8$fFE7$$\"3+b,'\\*[J.9Fegl$\"3Q1UXG+dnfFE7$$ \"3g!**eh=d!39Fegl$\"3ah1WbNR!*fFE7$$\"3@EyNx%*z79Fegl$\"3#pG&z:wu**fF E7$$\"3<2(*3Qlv<9Fegl$\"3')ek/kX5&*fFE7$$\"3I)e@))f8FU\"Fegl$\"3k3/C(3 Ld(fFE7$$\"3WpMbf1nF9Fegl$\"3==u4w2oTfFE7$$\"3S]`G?xiK9Fegl$\"3g#zf$)G JI*eFE7$$\"3n7\"\\<%=aU9Fegl$\"3?eX#zUaCv&FE7$$\"3wuG@jfX_9Fegl$\"3#>Z p<5$QbbFE7$$\"3oot%\\pT=Z\"Fegl$\"3&H64FxhY,&FE7$$\"3gi=oEuA\"\\\"Fegl $\"3!Q\">p%fvgG%FE7$$\"3Xm\"FE7$$\"3'HgUW.*)3h\"F egl$!3`')e#HTK;M#FE7$$\"3E&z#)Rp72j\"Fegl$!3eN.uZ@r$Q$FE7$$\"3#z)H_`j` ];Fegl$!3?!)))G0XD$H%FE7$$\"3I*yMyB_(o;Fegl$!3cmO+E-^\")\\FE7$$\"3/\"f Y@7opo\"Fegl$!3!e&>k8o#\\]&FE7$$\"3])*zo^oS(p\"Fegl$!3\\*Hnb/QOs&FE7$$ \"3&fSH7eXyq\"Fegl$!3;FU=#3P+)eFE7$$\"3]4,+Y\\18wz.JMfFE7$ $\"3083x5VG=2u7Etcv&FE7$ $\"3c_N)o8pgw\"Fegl$!3I0I=7#ywc&FE7$$\"3IB[.,&yfy\"Fegl$!3f&)*Rxa,a,&F E7$$\"3.%4'=ly)e!=Fegl$!3m7KK:)y\\E%FE7$$\"3u%[cqmV\\#=Fegl$!3E7^t[`W) Q$FE7$$\"35vo#*o%**R%=Fegl$!3c=tj>8C*Q#FE7$$\"3;c^p*\\QU&=Fegl$!3W^7au \"zT\"=FE7$$\"3cPMYIvZk=Fegl$!3b.\"pM>9,A\"FE7$$\"3)*= " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Ex ample 2" }}{PARA 0 "" 0 "" {TEXT -1 63 "This example constructs an ani mation of the area function for " }{XPPEDIT 18 0 "f(x) = 3*sin(x)+cos (2*x);" "6#/-%\"fG6#%\"xG,&*&\"\"$\"\"\"-%$sinG6#F'F+F+-%$cosG6#*&\"\" #F+F'F+F+" }{TEXT -1 17 " on the interval " }{XPPEDIT 18 0 "[0, 2*Pi]; " "6#7$\"\"!*&\"\"#\"\"\"%#PiGF'" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 26 "( Redraw with the option \"" }{TEXT 285 17 "areafunction= true" }{TEXT -1 28 "\" to obtain the animation. )" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "areaplot(3*s in(x)+cos(2*x),x=0..2*Pi,\n areafunction=false,color=[blue,gold,br own]);" }}{PARA 13 "" 1 "" {GLPLOT2D 483 311 311 {PLOTDATA 2 "6/-%'CUR VESG6$7%7$$\"\"!F)$\"\"\"F)F'F'-%'COLOURG6&%$RGBGF(F(F*-F$6$7>F'7$$\"3 #*4@;)eb&p8!#=$\"3-S>XkPIs8!#<7$$\"3!\\-[Ce)>hDF6$\"3zmB#)GcjJ;F97$$\" 3a=FdfdK,RF6$\"3GBjfM,m^=F97$$\"3!)4d`phL]_F6$\"3_81N3!R7+#F97$$\"3e)* 4]o\\$Hf'F6$\"3cu5*\\q>s3#F97$$\"3\"*f4v>fpPyF6$\"3/cKNZ*>67#F97$$\"3f X@S&ytl7*F6$\"3\\>+zKjh@@F97$$\"3MWJI?F97$$\"3: siveO(eV\"F9$\"3S\"=a02B*3?F97$$\"3i#y2QV$Rr:F9$\"3mB$o#y,++?F97$$\"3g Eh2m'puq\"F9$\"3IE2()\\8:4?F97$$\"3vh$z,L/'Q=F9$\"3)H&>@k`5L?F97$$\"3' [V5\"orod>F9$\"3y*Qg3)p)H1#F97$$\"3Uh\"\\.=)G*4#F9$\"3UFdH)Q/#*4#F97$$ \"3z;2b6GC>AF9$\"3Hh(>Unx07#F97$$\"3#*[1Mk&y(eBF9$\"3cU-SV(**47#F97$$ \"3'z:$)*[8H#[#F9$\"3-:]v(4Bs3#F97$$\"3/w#f%\\W!yh#F9$\"3Gj/8()R;+?F97 $$\"3ui#pr'\\%ou#F9$\"3-E(ebcHz&=F97$$\"3%pQg,@&[\")GF9$\"3*f[9Y`l#R;F 97$$\"3[\"GhL)p70IF9$\"3%f>GwP76P\"F97$$\"3L===R8\\QJF9$\"3#[.p?p%G45F 97$$\"3)e)*4NU>qF$F9$\"33,!ybAL]e&F67$$\"39\\f9G&3wR$F9$\"37I\\6[%f17 \"F67$$\"0&y'\\h&>EM!#9$!#;!#:F,-F$6$7BFat7$$\"3sk#*zk![y_$F9$!35dRZV_ 1STF67$$\"3cq*4,D)RiOF9$!3gtL][;2z)*F67$$\"3Es$QlNHSz$F9$!3O`M>?Mde:F9 7$$\"3nRKN?#*Q@RF9$!3#o*fq%Q,#)4#F97$$\"3#HId[j+G1%F9$!3%\\Z#p%[WF9$!3I#=\"\\')=-gPF97$$\"3\\mYOq)pc^%F9$!31>PMmdtlQ F97$$\"3[_'HN\\qGe%F9$!3.yBA.(4:%RF97$$\"3zl_>od[9YF9$!3IO(GX,Dl'RF97$ $\"35z3'G/,hk%F9$!3!4I>.'fj%)RF97$$\"3U#\\EvJ;xn%F9$!3w4gemMz&*RF97$$ \"3t0@>#fJ$4ZF9$!3y8-R$Gn***RF97$$\"3%=*\\uj'yBu%F9$!3=5DU1G&o*RF97$$ \"3%)yyHNdUvZF9$!3))43u!y/h)RF97$$\"3%ew]o!GZ3[F9$!3kRB%f/bx'RF97$$\"3 %>l.%y)>:%[F9$!3S?l'*Hz&=%RF97$$\"3i5!*>%)*Qh!\\F9$!33z_6oRspQF97$$\"3 IpV***3e2(\\F9$!3#RTvK;f)pPF97$$\"3XudN?&eg5&F9$!3sT#eDmC>&*4f\"F97$$\"3usgI0'=Gp&F9$!3AI2am/v*G\"F97$$\"3I*)ofN,Ti dF9$!3W>Lr[Yvx)*F67$$\"3s^c*)HOlCeF9$!37!on+j=u>(F67$$\"3C8W>Cr*o)eF9$ !3#=)\\v7sxfXF67$$\"0`,eM#e)*fFdt$\"\"*Fgt-F-6&F/$\"$+)!\"$$\"$)\\Fj^l $\"$'>Fj^l-F$6$7'Fa^l7$$\"3'\\Qk&=ii>gF9$\"3[G+uK\">0F)!#>7$$\"3azss(* [mYhF9$\"3'y))y)z;lYbF67$$\"3?+++3`=$G'F9$\"3@T7Y-+++5F97$$\"+3`=$G'! \"*$\"0ChC++++\"FdtF,-F$6$7$Fb`lFb`lF,-%)POLYGONSG6%747$$\"0!*Q!pr'p&y FgtF)7$F(F)F'F'F3F:F?FDFIFNFSFXFgnF\\oFaoFfoFfo7$$\"0y2QV$Rr:FdtF)-%&S TYLEG6#%,PATCHNOGRIDG-F-6&%$HSVG$\")nmmm!\")$\"0+++++++#Fgt$\"0+++++++ \"Fdt-F\\al6%767$$\"0\"yQCXz)\\#FdtF)FcalFfoF[pF`pFepFjpF_qFdqFiqF^rFc rFhrF]sFbsFgsF\\tFatFat7$FbtF)FfalFjal-F\\al6%7G7$$\"0o%Q!)*)Q7ZFdtF)F jblFatFatF[uF`uFeuFjuF_vFdvFivF^wFcwFhwF]xFbxFgxF\\yFayFfyF[zF`zFezFjz F_[lFd[lFi[lF^\\lFc\\lFh\\lF]]lFb]lFg]lF\\^lFa^lFa^l7$Fb^lF)Ffal-F-6&F \\bl$\")MLL$)Fe`l$\"0-_Ut*zn7Fgt$\"0++GS^[g*Fgt-F\\al6%7,7$$\"0w+p#Q)3 9'FdtF)FaclFa^lFa^lFb_lFh_lF]`lFb`lFb`l7$Fc`lF)FfalFjal-F$6%7$FbalF'-% &COLORG6&F/$\"\"$!\"\"FgdlFgdl-%*LINESTYLEG6#F+-F$6%7$F`dlFb`lFddlFjdl -%+AXESLABELSG6$%\"xGQ!6\"-%%VIEWG6$;F(Fc`l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3 " "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 1 0" "Curve 11" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Exampl e 3" }}{PARA 0 "" 0 "" {TEXT -1 61 "This example constructs an animati on of the area function for" }}{PARA 257 "" 0 "" {TEXT -1 3 " " } {XPPEDIT 18 0 "f(x) = sin(x)+sin(3*x)/2+sin(5*x)/7;" "6#/-%\"fG6#%\"xG ,(-%$sinG6#F'\"\"\"*&-F*6#*&\"\"$F,F'F,F,\"\"#!\"\"F,*&-F*6#*&\"\"&F,F 'F,F,\"\"(F3F," }{TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 16 "on the interval " }{XPPEDIT 18 0 "[0, 6*Pi];" "6#7$\"\"!*&\"\"'\"\"\"%#PiGF' " }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 26 "( Redraw with the op tion \"" }{TEXT 285 17 "areafunction=true" }{TEXT -1 28 "\" to obtain \+ the animation. )" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 106 "areaplot(sin(x)+sin(3*x)/2+sin(5*x)/7,x=0..6* Pi,\n areafunction=false,color=[blue,gold,brown],frames=20);" }} {PARA 13 "" 1 "" {GLPLOT2D 617 360 360 {PLOTDATA 2 "6B-%'CURVESG6$7%7$ $\"\"!F)F(F'F'-%'COLOURG6&%$RGBG$\"$+)!\"$$\"$)\\F0$\"$'>F0-F$6$7$F'F' F*-F$6$7TF'7$$\"3#Q0=XXLe8&!#>$\"3=xwX)*\\^V;!#=7$$\"3w5O!4pmr-\"FA$\" 3!)Hv%=;-PC$FA7$$\"33;aNO+vS:FA$\"33a.&RQG#fZFA7$$\"3_@s!=QLV0#FA$\"3[ 2t$yYPE:'FA7$$\"3)p-fss;zc#FA$\"3]>.UiT,#R(FA7$$\"3;K3rs+]\"3$FA$\"33y ]i>zL_%)FA7$$\"3'yji\"=M3&f$FA$\"3YR03TLX;$*FA7$$\"30VWhjnm3TFA$\"3Wv. a3ygv**FA7$$\"3'H$oP')G`bXFA$\"33bf<,l>Q5!#<7$$\"3UB#R\"4!*R-]FA$\"3u \"*Qe`vwj5Fdo7$$\"3l=/_q?$eA&FA$\"3o6[^\"yt62\"Fdo7$$\"3)Qh,>8l#\\aFA$ \"3Un7YHo=v5Fdo7$$\"354GG$>)pscFA$\"3%[AOYtyf2\"Fdo7$$\"3M/Sma78'*eFA$ \"37x)4=sSP2\"Fdo7$$\"39%y)=+N')*y'FA$\"3%oic+*)[)Q5Fdo7$$\"31lNrXdf$o (FA$\"3DK%eK$**eS(*FA7$$\"3aHS(4^'y$p*FA$\"3-ln:FPQ')zFA7$$\"3S\\MiFxR q6Fdo$\"3#G?r\"p*ed!oFA7$$\"3aEj)zh&)4A\"Fdo$\"37rB&Ge^2l'FA7$$\"3o.# \\$3Ndr7Fdo$\"3w+%[)*Hv]a'FA7$$\"3g!37()Rh@K\"Fdo$\"3E/))paX#)zkFA7$$ \"3ud\\2*G\\FP\"Fdo$\"3zH\\ZL2%\\W'FA7$$\"3#=r+)p]#RZ\"Fdo$\"3(Hv[ZODq U'FA7$$\"33mk_]35v:Fdo$\"33w+A=[cGkFA7$$\"3m%\\F/w&zv;Fdo$\"3tj'o:y?rU 'FA7$$\"3EB&G.n!\\wFdo$\"3gAb[Z?) )omFA7$$\"3?!eI,\\!)y(>Fdo$\"3g@l?E7KIoFA7$$\"3U_%yFj%fk@Fdo$\"3NSD65j 4EzFA7$$\"3)[KEax38N#Fdo$\"3+!=8:QSVb*FA7$$\"3m]'H`huzW#Fdo$\"3\\8/&4L j)H5Fdo7$$\"3*f(HBb/kWDFdo$\"3#f08\\LzB2\"Fdo7$$\"3K2)3_\"p!)oDFdo$\"3 u()HwJ,qv5Fdo7$$\"3mQY=vL(Hf#Fdo$\"3mR6f-]`v5Fdo7$$\"3Wq/;N)Rrh#Fdo$\" 3Qr$H!>ujr5Fdo7$$\"3x,j8&H18k#Fdo$\"3GY\"p8e'yj5Fdo7$$\"3)['z3:#R'*o#F do$\"3rQ!3,A!\\N5Fdo7$$\"3cF'R]8szt#Fdo$\"3/ndFxh7&*)*FA7$$\"3g$f%**4 \"ezy#Fdo$\"3B05t)f;zA*FA7$$\"32g&\\\\3Wz$GFdo$\"3![**>RfcqO)FA7$$\"3c EX!*f+$z)GFdo$\"3#3a2t[49K(FA7$$\"3g#\\f[.;z$HFdo$\"3jq(eu;ct5'FA7$$\" 33fW\")4?!z)HFdo$\"3+T;ISiH[ZFA7$$\"3cD%pZ)z)y.$Fdo$\"37\"\\Sq#HytKFA7 $$\"3g\"RC(fR(y3$Fdo$\"3@8G$>pL$=\"F>7$$\"0z*e`EfTJ!#9$\"0ocuxx/qJrFA7$$\"3/?aZ]R\"oV$Fdo$!3'*f&[*oQO.#)FA 7$$\"3yjZx>'Rm[$Fdo$!3!\\uXH\")[O4*FA7$$\"3^2T2*Glk`$Fdo$!3W>43t6\\#z* FA7$$\"3+P 0tNb2\"Fdo7$$\"3453Pxm%er$Fdo$!3]`*\\KA&fv5Fdo7$$\"32DY)**es9u$Fdo$!3i &3`u(Hvr5Fdo7$$\"3h$))R/CwR%QFdo$!3(32&y,\\7C5Fdo7$$\"3iU^*3*)zk%RFdo$ !3?*>_!pIyE%*FA7$$\"3qE\\7L/0FTFdo$!3)*)>KWP].'yFA7$$\"3y5ZNv4i2VFdo$! 3=dX#[\"**p@oFA7$$\"31V#))4*3WeVFdo$!3%\\O82Bp9m'FA7$$\"3Lv(eBB$p\\Fdo$!3uj-@%Rt\")['FA7$$\"3_q<'H#=N?]Fdo$!3'R IhS@u,c'FA7$$\"3#4d^+T!Qr]Fdo$!3sVJy&*z)\\n'FA7$$\"3Kr89(**3C7&Fdo$!35 FvBY1UToFA7$$\"3c\"[aK*46>`Fdo$!3v*[wZ$*H*G!)FA7$$\"3o#fn$*)H\"e^&Fdo$ !3--?o3zz[(*FA7$$\"3yWpz<^70cFdo$!3%RLP&o8RR5Fdo7$$\"3'oHEiCPWp&Fdo$!3 !*)ox?F\")Q2\"Fdo7$$\"3!\\jL$y_w;dFdo$!3#e5D!4`+w5Fdo7$$\"3$H(4W5L4RdF do$!3%4g!o\")f4v5Fdo7$$\"3'4J[DM@9w&Fdo$!3ILiIOJ'42\"Fdo7$$\"3)*[clu$ \\Py&Fdo$!3e6K:SeVj5Fdo7$$\"3.D.()QaSGeFdo$!3c(fp,MBw.\"Fdo7$$\"3'>+&3 .:1teFdo$!3YZFJ=kiB.'Fdo$!3CXxfHevcsFA7$$\"3?>!)R@IY&3 'Fdo$!3WHJY3oa_fFA7$$\"3&RFw4Sj&QhFdo$!3IU@+iNS)[%FA7$$\"3!y_a0yj;>'Fd o$!3a+.x^Zs+HFA7$$\"3p\"yK,;kZC'Fdo$!3Dm8Vc2\">B\"FA7$$\"0fzrI&=$G'F[ \\l$\"0Y'R'e-nM$!#GF*-F$6$7UFa[m7$$\"3WO5rRX'yH'Fdo$\"3l?[*>E>mr%F>7$$ \"3su?SEv%GM'Fdo$\"3WU\\n?qH1>FA7$$\"377J480$yQ'Fdo$\"3S>8Fe\"*Q-LFA7$ $\"3^\\Ty*\\8GV'Fdo$\"3OwE@.TLKYFA7$$\"3#p=vk['zxkFdo$\"3+3P\"=w`3(eFA 7$$\"3JCi;t%zF_'Fdo$\"3;ReJ,'fe*pFA7$$\"3qhs&)fCwnlFdo$\"33>]g(yy\"*)z FA7$$\"35*H[lWXFh'Fdo$\"3'zfW7rc<'f\\\"zFA7$$\"3](>p`/uoW( Fdo$\"3Rw8DH!4/$oFA7$$\"3Cep.e9p(\\(Fdo$\"3+JPz^ZonmFA7$$\"3)*=Zqq)3&[ vFdo$\"3yfZwEjublFA7$$\"3%)yCP$GE$*f(Fdo$\"3Q&Gf^(oz&['FA7$$\"3eR-/'pV ,l(Fdo$\"3#z6#ow7sZkFA7$$\"3=gdP@&y]zFdo$\"3t4mCgC-FkFA7$$\"3!z=NK7 up/)Fdo$\"3kdhEm1tUkFA7$$\"3cjhOtkFA7$$\"3DRr\\6 XvV\")Fdo$\"3q`ok@#4,`'FA7$$\"3o;\"GcqW@>)Fdo$\"3&*pE^5MMAmFA7$$\"3P#4 f(**[`S#)Fdo$\"3'H.b8)3+enFA7$$\"3%=#H?k_\\U%)Fdo$\"3mJ@2bb([)yFA7$$\" 3b\\nkGcXW')Fdo$\"38lVM09&)R'*FA7$$\"3(>uF&ep=P()Fdo$\"3M\")[^&RdO.\"F do7$$\"3QM(3%)G=*H))Fdo$\"3KrB7)3)zs5Fdo7$$\"3/#)*y37,J&))Fdo$\"3Mo-!= $3xv5Fdo7$$\"3[J#\\L&RGw))Fdo$\"3'pX'*\\iCb2\"Fdo7$$\"3!4[>eym%**))Fdo $\"3Q3nrVB%=2\"Fdo7$$\"3eG(*G='\\E#*)Fdo$\"3aeWbq'GX1\"Fdo7$$\"3!RAIKG :!p*)Fdo$\"3!o\"oT&*3NQ5Fdo7$$\"3+@2<[4Q:!*Fdo$\"3MY'=IC;'f**FA7$$\"3[ 5Gf\"e#Rl!*Fdo$\"3CyUf\\ui9$*FA7$$\"3<)*[,:US:\"*Fdo$\"3qu#3#G4Ev%)FA7 $$\"3'e)pV[eTl\"*Fdo$\"3=*ys!4[^\\uFA7$$\"3dt!f=[Fa@*Fdo$\"3IM6cPG&HD' FA7$$\"3Eh6G:\"RaE*Fdo$\"3vPJ7azC3\\FA7$$\"3u]Kq[2X:$*Fdo$\"3]1RH7]NWM FA7$$\"3AS`7#QiaO*Fdo$\"3!G=QXW_`*=FA7$$\"3\"zUZb,uaT*Fdo$\"3uy3(Q_>,* HF>7$$\"0Qp2'zxC%*F[\\l$\"0tw*[v^3>Ff[mF_\\l-F$6$7SF_[n7$$\"3cm%fr/AuY *Fdo$!3+G\\aZt_m8FA7$$\"3)p]r(y+P>&*Fdo$!3W*oWELu^*HFA7$$\"3SZNQ5\"=8d *Fdo$!3$=%*GF4&oVXFA7$$\"31'e&*>9mKi*Fdo$!3I!Q)e\"ztD(fFA7$$\"3qCwgtT@ v'*Fdo$!3U\"f_.\"f\"zC(FA7$$\"3Nj'>_?irs*Fdo$!3?-Tk`E$GM)FA7$$\"3+-<$o B5\"z(*Fdo$!3w`&zR?u&Q#*FA7$$\"3UUPWo#e5$)*Fdo$!3sOE53Z9D**FA7$$\"3#Gj sE=zi()*Fdo$!3&zL4zIV^.\"Fdo7$$\"3Y@:!p4+:#**Fdo$!3+.!4M:#Gi5Fdo7$$\"3 bnf,a06W**Fdo$!3_JeEE5Jq5Fdo7$$\"3)=TI6,@n'**Fdo$!3=\"e&)3GT[2\"Fdo7$$ \"3=c[Co9L*)**Fdo$!3qh$)\\J#[g2\"Fdo7$$\"3BIf`#>%>,5!#;$!33L%**\\jFT2 \"Fdo7$$\"3J35F[`n$!3a1L8B `=V(*FA7$$\"3\"zL@()[=)Q5F[`n$!3PI^iScJM!)FA7$$\"3g*=:#>WNe5F[`n$!3!R5 \"G>58\\oFA7$$\"3GqK;^+Sj5F[`n$!3y#\\(eQb5#o'FA7$$\"39^86$oX%o5F[`n$!3 GZ9y:2$fc'FA7$$\"3)>Vf]J\"\\t5F[`n$!3KkT^i0?#\\'FA7$$\"3m7v+Zp`y5F[`n$ !3y'4#f$f,6X'FA7$$\"3?uO!4@G')3\"F[`n$!3M9*3L=@sU'FA7$$\"3sN)*zu%>()4 \"F[`n$!3,H;X`kaGkFA7$$\"3#4()zx!=f36F[`n$!3[\"zDkICqU'FA7$$\"3&f!*f29 k%=6F[`n$!3DXt!QEZ6W'FA7$$\"3YB*\\sI+M7\"F[`n$!3qbrP;LnqkFA7$$\"3(4%*R PZO$G6F[`n$!3xl[`MI9FlFA7$$\"3\\e*H-ksK8\"F[`n$!36v0xV#)**>mFA7$$\"3=w *>n!)3#Q6F[`n$!3')fN+$fqyv'FA7$$\"3S_\")G'y7t:\"F[`n$!3uVY6XB+,yFA7$$ \"3WGj&ew;k<\"F[`n$!3ye#4oH,/X*FA7$$\"3_#)=%>iAq=\"F[`n$!3rm%)*3sN#G5F do7$$\"3wOu-y%Gw>\"F[`n$!332cCI@mt5Fdo7$$\"3=D)[?%*z-?\"F[`n$!3OW(HSEi g2\"Fdo7$$\"3y8-219$H?\"F[`n$!3;y$)[n+:u5Fdo7$$\"3R-;4qGe07F[`n$!3Iqb$ \\59w1\"Fdo7$$\"3*4*H6MVB37F[`n$!3)zfo6c#=c5Fdo7$$\"3.od:is`87F[`n$!3j $>[%fKx<5Fdo7$$\"31X&)>!>S)=7F[`n$!3]/PkE2\"po'ycFA7$$\"39&)prtZm U7F[`n$!3I'G)*f5*[YVFA7$$\"3;t1U!pHuC\"F[`n$!3@\"zXJ$*Hx\"HFA7$$\"3=hV 72Y>_7F[`n$!37[&)GD=@B9FA7$$\"0#fVhqjc7!#8$\"0#Hzs^S$p)Ff[mF*-F$6$7TFc jn7$$\"3O\\!GQ_fpD\"F[`n$\"3#eW(=y\"ok.\"F>7$$\"3_U.Y*3Z?E\"F[`n$\"3,R .:8.UIN(R#G\"F [`n$\"3ts^zb,@5uFA7$$\"3[3=i<\\[(G\"F[`n$\"3-u:otL]e%)FA7$$\"3k,TD$[sD H\"F[`n$\"3<^&pyakTJ*FA7$$\"3![R'))[+m(H\"F[`n$\"3OI.j2%*po**FA7$$\"3r $=5&R,F-8F[`n$\"3*R#HY?\"o(Q5Fdo7$$\"3jsR8I-)oI\"F[`n$\"3End*\\d[Y1\"F do7$$\"34neWv_=48F[`n$\"3W.9\"\\c#)=2\"Fdo7$$\"3bhxv?.\\68F[`n$\"316b= Ky_v5Fdo7$$\"3,c'pgO&z88F[`n$\"3)[ijTZwd2\"Fdo7$$\"3Z]:Q6/5;8F[`n$\"3' 4))Rn*=%G2\"Fdo7$$\"3KG\"HEf?`K\"F[`n$\"3?M$H?4CT.\"Fdo7$$\"3)fqwQxSXL \"F[`n$\"3#[TqH\"=y]'*FA7$$\"3gB>#3'4qa8F[`n$\"3iCw#GNVw*yFA7$$\"3ATrw Z6'[P\"F[`n$\"3Q)Gf^1^Yw'FA7$$\"3+xf'*QMgz8F[`n$\"3L`%Hj1U$HmFA7$$\"3g 7[;IdM%Q\"F[`n$\"3dIX+Oi]/$QlJXkFA7$$\"3+b,'\\*[J.9F[`n$\"3NF1DzH5FkFA 7$$\"3@EyNx%*z79F[`n$\"3P$RD%H:aGkFA7$$\"3I)e@))f8FU\"F[`n$\"3)o-e!)*f -FkFA7$$\"3S]`G?xiK9F[`n$\"3'fMPJ0k6W'FA7$$\"3`Js,\"y%eP9F[`n$\"3?fU&3 8&)3Z'FA7$$\"3n7\"\\<%=aU9F[`n$\"3R'[$*=dFy_'FA7$$\"3i$*4[-*)\\Z9F[`n$ \"3.qA/#G]:i'FA7$$\"3wuG@jfX_9F[`n$\"3S&[9J`y2w'FA7$$\"3oot%\\pT=Z\"F[ `n$\"3)[Li&)4T!HyFA7$$\"3gi=oEuA\"\\\"F[`n$\"3dV.t5Fdo7$$ \"3]/0Iu$fS^\"F[`n$\"3C4&Q!H`(f2\"Fdo7$$\"3bU#ptD'f;:F[`n$\"3a\"fbV][[ 2\"Fdo7$$\"3g!)zVSJ8>:F[`n$\"3!=)HT6#R&p5Fdo7$$\"3Z=n]B+n@:F[`n$\"3I@@ &fs,)f5Fdo7$$\"3S%>W'*yVn_\"F[`n$\"35$ozd]Xi-\"Fdo7$$\"3]q;ybv\"=`\"F[ `n$\"3Vhh/n`\"F[`n$\"3rb;)*yG6F!*FA7$$\"3eo_UN3fT :F[`n$\"3I*4mEV509)FA7$$\"3inqCvuZY:F[`n$\"3m)RrQ7#G!3(FA7$$\"3om)o]6k 8b\"F[`n$\"3[6Z6qcBjeFA7$$\"3sl1*[v]ib\"F[`n$\"3eG#*QrIX7XFA7$$\"3wkCr %RP6c\"F[`n$\"3em1J%yck0$FA7$$\"3!QEMX.Cgc\"F[`n$\"3*3*>-C95G:FA7$$\"0 !\\zEjzq:Ffjn$!07*fYcn'3\"!#FF_\\l-F$6$7UF\\jo7$$\"3%G1cVn54d\"F[`n$!3 54`:g#\\an$!#?7$$\"3S!)oOpz!fd\"F[`n$!3u]W`4<%ej\"FA7$$\"3'zpxVE04e\"F [`n$!3g4f4c*)3%>$FA7$$\"3M:&)QfD!fe\"F[`n$!3YGq)zbdLn%FA7$$\"3!HL*Ra)* *3f\"F[`n$!3QuBoX[$*QgFA7$$\"3Y],T\\r*ef\"F[`n$!3A)\\M2)o*4E(FA7$$\"3% y'4UWW*3g\"F[`n$!3T$eX;#=\"eJ)FA7$$\"3B&yJ%R<*eg\"F[`n$!3Edvx)GAm=*FA7 $$\"3'HgUW.*)3h\"F[`n$!35NER_P;k)*FA7$$\"3/^wK\\\\%eh\"F[`n$!3)4N'36!f V.\"Fdo7$$\"36*p7U'3!3i\"F[`n$!3e-F19xoj5Fdo7$$\"3(HAb;#)yKi\"F[`n$!3% )oa*Q(osr5Fdo7$$\"3>Zx4znvD;F[`n$!3#fM;d78c2\"Fdo7$$\"3Sr-aOZBG;F[`n$! 3G:Dn5`ev5Fdo7$$\"3E&z#)Rp72j\"F[`n$!3UH]c_0\">2\"Fdo7$$\"3T\"*GvBXiS; F[`n$!3Vo#oG!=%o-\"Fdo7$$\"3#z)H_`j`];F[`n$!3Yku)**)[Z#\\*FA7$$\"3I*yM yB_(o;F[`n$!36*)>]QOZ'FA7$$\"3c>2u7EtcNch'FA7$$\"3c_N)o8pgw\"F[`n$!3$Q.IiHxH u'FA7$$\"3IB[.,&yfy\"F[`n$!3Xs7Ox,LFyFA7$$\"3.%4'=ly)e!=F[`n$!3!f\")zy UO4b*FA7$$\"3@*G@hw:a\"=F[`n$!3bM1%*p'=(G5Fdo7$$\"3u%[cqmV\\#=F[`n$!3y 5nO0(*pr5Fdo7$$\"3j$G!HUcKF=F[`n$!3umo+BxUv5Fdo7$$\"3^#3Cvh2(H=F[`n$!3 ;hrJrd!e2\"Fdo7$$\"3/\")yv#f*3K=F[`n$!3!Q%ox/Vfs5Fdo7$$\"3#*z;*zcrW$=F [`n$!3)*o(=$Rvdl5Fdo7$$\"3Lx#f%=bBR=F[`n$!3\">_#)eI-%R5Fdo7$$\"35vo#*o %**R%=F[`n$!39C510:Th**FA7$$\"3i:5J%)*=\"\\=F[`n$!3]5L'yIY%*H*FA7$$\"3 ;c^p*\\QU&=F[`n$!3%yhh!ys\"RV)FA7$$\"3o'Hz],e$f=F[`n$!3I&[pL@oOP(FA7$$ \"3cPMYIvZk=F[`n$!3m!RK^%R$e8'FA7$$\"3Wyv%e/(fp=F[`n$!31/,cYMIXZFA7$$ \"3)*=7$$\"03\"*3R6( \\bF[\\lF)Fg^qF^dlFcdlFhdlF]elFbelFgelF\\flFaflFfflF[glF`glFeglFjglF_h lFdhlFihlF^ilFcilFhilF]jlFbjlFgjlF\\[mFa[mFa[m7$Fb[mF)Fb[qFh]q-Fgjp6%7 @7$$\"0oxU\">[]zF[\\lF)Fb[qFf[q-Fgjp6%7?7$$\"0Jry%e[(o)F[\\lF )F``qFgcmF\\dmFadmFfdmF[emF`emFeemFjemF_fmFdfmFifmF^gmFcgmFhgmF]hmFbhm FghmF\\imFaimFfimF[jmF`jmFejmFjjmF_[nF_[n7$F`[nF)Fb[qFf[q-Fgjp6%7?7$$ \"0I!\\.Ib:5FfjnF)Fi`qF_[nF_[nFg[nF\\\\nFa\\nFf\\nF[]nF`]nFe]nFj]nF_^n Fd^nFi^nF^_nFc_nFh_nF^`nFc`nFh`nF]anFbanFganF\\bnFabnFfbnFfbn7$$\"0n.4 @G')3\"FfjnF)Fb[qFh]q-Fgjp6%7)7$$\"0xT$4+h)4\"FfjnF)F`aqFfbnF[cnF`cnF` cn7$$\"0()zx!=f36FfjnF)Fb[qFh]q-Fgjp6%7>7$$\"0!zgMWh#=\"FfjnF)FiaqF`cn FecnFjcnF_dnFddnFidnF^enFcenFhenF]fnFbfnFgfnF\\gnFagnFfgnF[hnF`hnFehnF jhnF_inFdinFiinF^jnFcjnFcjn7$FdjnF)Fb[qFh]q-Fgjp6%7@7$$\"0/)>yf(*H8Ffj nF)FbbqFcjnFcjnF\\[oFa[oFf[oF[\\oF`\\oFe\\oFj\\oF_]oFd]oFi]oF^^oFc^oFh ^oF]_oFb_oFg_oF\\`oFa`oFf`oF[aoF`aoFeaoFjaoF_boF_bo7$$\"0;g\\*[J.9Ffjn F)Fb[qFf[q-Fgjp6%7)7$$\"0)3*oC9IT\"FfjnF)FibqF_boFdboFiboFibo7$$\"0f@) )f8FU\"FfjnF)Fb[qFf[q-Fgjp6%7>7$$\"0C3G'\\v'\\\"FfjnF)FbcqFiboF^coFcco FhcoF]doFbdoFgdoF\\eoFaeoFfeoF[foF`foFefoFjfoF_goFdgoFigoF^hoFchoFhhoF ]ioFbioFgioF\\joF\\jo7$F]joF)Fb[qFf[q-Fgjp6%7@7$$\"0'Gy=.aW;FfjnF)F[dq F\\joF\\joFejoF[[pF`[pFe[pFj[pF_\\pFd\\pFi\\pF^]pFc]pFh]pF]^pFb^pFg^pF \\_pFa_pFf_pF[`pF``pFe`pFj`pF_apFdapFiapFiap7$$\"0\"3x5VG= " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Example 4" }}{PARA 0 "" 0 "" {TEXT -1 63 " This example constructs an animation of the area function for " } {XPPEDIT 18 0 "f(x) = abs(x^2-4)-2;" "6#/-%\"fG6#%\"xG,&-%$absG6#,&*$F '\"\"#\"\"\"\"\"%!\"\"F/F.F1" }{TEXT -1 17 " on the interval " } {XPPEDIT 18 0 "[-3,3]" "6#7$,$\"\"$!\"\"F%" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 26 "( Redraw with the option \"" }{TEXT 285 17 "areaf unction=true" }{TEXT -1 49 "\" to obtain an animation for the area fun ction. )" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "areaplot(abs(x^2-4)-2,x=-3..3,color=[blue,green,brown ],\n areafunction=false);" }}{PARA 13 "" 1 "" {GLPLOT2D 547 384 384 {PLOTDATA 2 "62-%'CURVESG6$7%7$$!\"$\"\"!$\"\"$F*F'F'-%'COLOURG6&%$RGB G$F*F*F1$\"\"\"F*-F$6$7,F'7$$!3&*****\\P&3Y$H!#<$\"3N*)yOos#>h#F:7$$!3 !******\\2<#pGF:$\"3]a:ZBmSKAF:7$$!3')**\\78.K7GF:$\"3:(\\:OaX\"4>F:7$ $!3#)***\\7bBav#F:$\"3CgJyY*eBf\"F:7$$!3'***\\(=>P9p#F:$\"3,&)z!y:MQC \"F:7$$!36++]K3XFEF:$\"36S%\\?xy\\.*!#=7$$!3w******H./jDF:$\"3%\\2l?Ld 7$$!3#****\\i3@/P#F:$!3 Y.PhQ(Q5\"QFV7$$!3/++vG\"))4J#F:$!3=Ndw(oQLf'FV7$$!3;++Dr^b^AF:$!3'o#Q <3J*\\I*FV7$$!3/++D'y:+>#F:$!3?%zvf&3$Q?\"F:7$$!3$****\\7Sw%G@F:$!3a\\ =K4#)ep9F:7$$!3=++D\"GK[1#F:$!3s>zI]wYOF:7$$!3!****\\([\"[x$>F:$!3e^S)z)y'[v\"F:7$$!3/++DO\"3V(=F:$!3d[H h*)4.8:F:7$$!3#******\\V'zViUC\"F:$\"3B?y$4!f6=XFV7$$!3-++DhkaI6F:$\"3-B5b*)pk=sFV7$$!3s* *****\\XF`**FV$\"3#HABtDB$45F:7$$!3u*******>#z2))FV$\"3S\">;c'zAC7F:7$ $!3S++]7RKvuFV$\"3uc?.C`>T9F:7$$!3s,+++P'eH'FV$\"3oA-r-5i.;F:7$$!3q)** *\\7*3=+&FV$\"3ib$Gg2>)\\F:7$$!32)***\\i6:.8FV$\"3+\\nZqz,$)>F:7$$!3W b+++v`hH!#?$\"3)ej&HH7****>F:7$$\"3]****\\(QIKH\"FV$\"3#fY[;bvK)>F:7$$ \"38****\\7:xWCFV$\"3]%o;D#4BS>F:7$$\"3E,++vuY)o$FV$\"3Er'eo2_R'=F:7$$ \"3!z******4FL(\\FV$\"3IcScv,m_:F:7$$\"30+]P\\`9Q>F:$ !3'4%RI&R2kv\"F:7$$\"3P+++!)RO+?F:$!3Ye&=v%Ra)*>F:7$$\"3A++D;:*R1#F:$! 3@D![3-R*Rw7#F:$!3O-!Ru;PKZ\"F:7$$\"3=+]i?(>2>#F:$!3?@ Zm0ru+7F:7$$\"3O++v)Q?QD#F:$!3;rza_l$H?*FV7$$\"3K+]P\\L!=J#F:$!3/)H&=Q FlblFV7$$\"3G+++5jypBF:$!3JHeO\\%G6%QFV7$$\"3B++DE8COCF:$!3_$)R;F+#GZ' Fho7$$\"0=$yU(*[\\CF^oF_oFjs-F$6$7-Fj_l7$$\"3<++]Ujp-DF:$\"35z(Gw#)*)[ j#FV7$$\"33++D,X8iDF:$\"3ske&\\-K`k&FV7$$\"3++++gEd@EF:$\"3#yv%f;@VE() FV7$$\"31+]PMh%\\o#F:$\"3)fD&\\Wd$*37F:7$$\"39++v3'>$[FF:$\"3[`(R=ngKb \"F:7$$\"39+++5h(*3GF:$\"31L2b'yY.*=F:7$$\"37++D6EjpGF:$\"3G%\\\\NK\"z MAF:7$$\"31+]i0j\"[$HF:$\"3KtBwZn98EF:7$F+F+FhblF--F$6$7$FhblFhblF--%) POLYGONSG6%717$$!0f\"Rr[uCFF^oF*7$F(F*F'F'F7F=FBFGFLFQFWFfnF[oF[o7$F\\ oF*-%&STYLEG6#%,PATCHNOGRIDG-F.6&%$HSVG$\")nmmm!\")$\"0+++++++#!#:$\"0 +++++++\"F^o-F]cl6%767$$!09yDl^=$>F^oF*FdclF[oF[oFcoFioF^pFcpFhpF]qFbq FgqF\\rFarFfrF[sF`sFesFes7$FfsF*Fecl-F.6&F[dl$\")LLLLF^dlF_dlFbdl-F]cl 6%7@7$F1F*FjdlFesFesF_tFdtFitF^uFcuFhuF]vFbvFgvF\\wFawFfwF\\xFaxFfxF[y F`yFeyFjyF_zFdzFizF^[lFc[lFc[l7$Fd[lF*FeclFicl-F]cl6%767$$\"09yDl^=$>F ^oF*FcelFc[lFc[lFi[lF^\\lFc\\lFh\\lF]]lFb]lFg]lF\\^lFa^lFf^lF[_lF`_lFe _lFj_lFj_l7$F[`lF*FeclF[el-F]cl6%727$$\"0f\"Rr[uCFF^oF*FjelFj_lFj_lF`` lFe`lFj`lF_alFdalFialF^blFcblFhblFhblFhbl7$F+F*FeclFicl-F$6%7$FcclF'-% &COLORG6&F0$F,FisFhflFhfl-%*LINESTYLEG6#F3-F$6%7$FaflFhblFeflFifl-%+AX ESLABELSG6$%\"xGQ!6\"-%%VIEWG6$;F(F+%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curv e 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Cur ve 11" "Curve 12" "Curve 13" "Curve 14" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Example 5" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 63 "This example constructs an animation of t he area function for " }{XPPEDIT 18 0 "f(x) = J[0](x);" "6#/-%\"fG6#% \"xG-&%\"JG6#\"\"!6#F'" }{TEXT -1 26 " on the interval [0, 20]. " }} {PARA 0 "" 0 "" {TEXT -1 26 "( Redraw with the option \"" }{TEXT 285 17 "areafunction=true" }{TEXT -1 49 "\" to obtain an animation for the area function. )" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "areaplot(BesselJ(0,x),x=[0..15.5,0..20],ytic kmarks=2,\n color=[purple,cyan,red],areafunction=false,areas=true);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6)%3signed~areas~...~~G$\"+V+Iq9!\"*$! +6@a9!)!#5$\"+b^A$*fF)$!+/i\\!*\\F)$\"+B6NlVF)$!+P$))[@$!#6" }}{PARA 13 "" 1 "" {GLPLOT2D 553 272 272 {PLOTDATA 2 "66-%'CURVESG6$7%7$$\"\"! F)$\"\"\"F)F'F'-%'COLOURG6&%$RGBG$\"\"%!\"\"F)$\"\"*F2-F$6$73F'7$$\"+S &)G\\a!#6$\"+\"pxD***!#57$$\"+3x&)*3\"F>$\"+#HF.(**F>7$$\"+ilyM;F>$\"+ S$)HL**F>7$$\"+$\"+kKd\"))*F>7$$\"+DJdpKF>$\"+'fFXt*F>7$$\"+M3V fVF>$\"+Xx\\I&*F>7$$\"+j&*)fD'F>$\"+T'R_/*F>7$$\"+#H[D:)F>$\"+#pghS)F> 7$$\"+%pU&G5!\"*$\"+vF1DvF>7$$\"+e0$=C\"F_o$\"+ijp+lF>7$$\"+LA`c9F_o$ \"++GUf`F>7$$\"+3RBr;F_o$\"+\\AzXTF>7$$\"+W^\"\\)=F_o$\"+Ot(e!HF>7$$\" +zjf)4#F_o$\"+%\\ZSn\"F>7$$\"+Qiq'H#F_o$\"+#f'*=t&F;7$$\"0x&pdb#[S#!#9 $\"0jJ6*HKP9!#HF,-F$6$797$Faq$\"0&R-)oQuV\"Ffq7$$\"+'4;[\\#F_o$!+*Rd.e %F;7$$\"+!QZ**p#F_o$!+E8EC9F>7$$\"+j'y]!HF_o$!+&[O@E#F>7$$\"+IdA(HF>7$$\"+'zs$HLF_o$!+a3+1NF>7$$\"+]h5NMF_o$!+DGI.PF>7$$\"+/&R3a $F_o$!+[S)Q&QF>7$$\"+eGdYOF_o$!+!))>w&RF>7$$\"+8iI_PF_o$!+!)f\"[,%F>7$ $\"+)3'o1QF_o$!+S1LESF>7$$\"+jf1hQF_o$!+yD'e-%F>7$$\"+ReW:RF_o$!+r=e8S F>7$$\"+9d#)pRF_o$!+wio*)RF>7$$\"+laeySF_o$!+Se(z!RF>7$$\"+<_M(=%F_o$! +:-%Gy$F>7$$\"+7l$*yVF_o$!+f%=YY$F>7$$\"+4y_qXF_o$!+!QLf.$F>7$$\"+HU@' y%F_o$!+/IBXCF>7$$\"+]1!>+&F_o$!+g&R(p7$$\"++FZ=_F_o$!+U)H%R5F>7$$ \"+]Z/NaF_o$!+(>!R7HF;7$$\"0J'G5\"y+_&Fcq$!0,s!y,%*3A!#I-F-6&F/F(F*F*- F$6$78Ffx7$$\"+]?vVcF_o$\"+_$R6:%F;7$$\"+]$fC&eF_o$\"+.J7y5F>7$$\"+'z6 :B'F_o$\"+A0n*3#F>7$$\"+1o(oX'F_o$\"+')4)>`#F>7$$\"+<=C#o'F_o$\"+(*[CL GF>7$$\"+z')pxnF_o$\"+!4fc\"HF>7$$\"+Ub:toF_o$\"+*\\e0(HF>7$$\"+tR)3#p F_o$\"+n$[w)HF>7$$\"+0ChopF_o$\"+f&Ry*HF>7$$\"+O3M;qF_o$\"+sm:,IF>7$$ \"+n#pS1(F_o$\"+%4Rw*HF>7$$\"+!y)e>rF_o$\"+p/-&)HF>7$$\"+#H3^<(F_o$\"+ MoLjHF>7$$\"+/yiIsF_o$\"+&fBF$HF>7$$\"+;t9'G(F_o$\"+([TL*GF>7$$\"+Sj=( R(F_o$\"+dj.*y#F>7$$\"+j`A3vF_o$\"+h!)=_EF>7$$\"+m?![q(F_o$\"+[.'oL#F> 7$$\"+n(y8!zF_o$\"+$*[fS>F>7$$\"+j.tK$)F_o$\"+yecF()F;7$$\"0,6H\"zs`') Fcq$\"0Rq$Qr>7$$\"+!G;cc*F_o$!+U+]S?F>7$$\"+WA(yx*F_o$!+Pii,BF>7$$\"+4#G ,***F_o$!+#=W\\X#F>7$$\"+yY_/5!\")$!+FLYwCF>7$$\"+Nl.55Fial$!+YNO!\\#F >7$$\"+#R[b,\"Fial$!+IZk'\\#F>7$$\"+]-1@5Fial$!+\"RH`\\#F>7$$\"+lR3K5F ial$!+]66qCF>7$$\"+!o2J/\"Fial$!+%)GL:CF>7$$\"+K+Ii5Fial$!+%=$\\_AF>7$ $\"+%Q#\\\"3\"Fial$!+9Af5?F>7$$\"+;*[H7\"Fial$!+$y9$p7F>7$$\"+qvxl6Fia l$!+@r!y6$F;7$$\"0V,RW`\"z6!#8$\"0fIk[2SF%FfqF\\y-F$6$73Fidl7$$\"+`qn2 7Fial$\"+'f'=jkF;7$$\"+cp@[7Fial$\"+h43R9F>7$$\"+#GB2F\"Fial$\"+'\\!Gv 7$$\"+3'HKH\"Fial$\"+*)f\"o,#F>7$$\"+v5M.8Fial$\"+okc\"4#F>7$$\"+UD X88Fial$\"+$QbW9#F>7$$\"+5ScB8Fial$\"+vf6v@F>7$$\"+xanL8Fial$\"+MyS$=# F>7$$\"+E;ZW8Fial$\"+v,nn@F>7$$\"+wxEb8Fial$\"+R!=p7#F>7$$\"+ER1m8Fial $\"+g2#=1#F>7$$\"+v+'oP\"Fial$\"+:F>7$$\"+3fU'R\"Fial$\"+'ehtv\"F> 7$$\"+S<*fT\"Fial$\"+&f5yZ\"F>7$$\"+&)Hxe9Fial$\"+u\\@JqF;7$$\"0y[3x\" 4$\\\"F\\el$!0&\\+And-HFfqF,-F$6$7&F]jl7$$\"+.o-*\\\"Fial$!+W;rA7F;7$$ \"+TO5T:Fial$!+l$y)*Q*F;7$$\"$b\"F2$!0]+!4lI#4\"!#:F\\y-F$6$7/F_[m7$$ \"+U9C#e\"Fial$!+6#*zg:F>7$$\"+u^x.;Fial$!+aP#=y\"F>7$$\"+1*3`i\"Fial$ !+,L9=>F>7$$\"+y'ycj\"Fial$!+qn!>&>F>7$$\"+]%[gk\"Fial$!+#e_X'>F>7$$\" +A#=kl\"Fial$!+X)yg&>F>7$$\"+$*zym;Fial$!+0#3n#>F>7$$\"+sr*zo\"Fial$!+ mjl.=F>7$$\"+^j?47$$\"+jMF^7$$\"+q( G**y\"Fial$!+:&[UA$F;7$$\"04\"z'R1r!=F\\el$!0$ondv7KUFfqF\\y-F$6$70F__ m7$$\"+9@BM=Fial$\"+!Q!o#*\\F;7$$\"+`v&Q(=Fial$\"+/P:T6F>7$$\"+W?)\\*= Fial$\"+3(e8T\"F>7$$\"+Ol5;>Fial$\"+*=ohh\"F>7$$\"+`f@E>Fial$\"+jI\\)o \"F>7$$\"+q`KO>Fial$\"+sECV7$$\"+(yMk%>Fial$\"+gE&*z7$$\"+/Uac>F ial$\"+IQM)z\"F>7$$\"+`\"3u'>Fial$\"+Dce(z\"F>7$$\"+-@Fy>Fial$\"+&o%pv 7$$\"+^g8*)>Fial$\"+8Q/L7$$\"#?F)$\"+VmCq;F>7$F_cm$\"0$eSVmCq;Fd [mF,-%)POLYGONSG6%787$$\"0)y%)yFT-7FcqF)7$F(F)F'F'F8F?FDFIFNFSFXFgnF\\ oFboFgoF\\pFapFfpF[qF`qF`q7$FaqF)-%&STYLEG6#%,PATCHNOGRIDG-F-6&%$HSVG$ \")tS2uFial$\"0++++++?#Fd[m$\"0+++++++\"Fcq-Fgcm6%7>7$$\"0/\"*R$=XiRFc qF)F^dmFjqFjqF]rFbrFgrF\\sFasFfsF[tF`tFetFjtF_uFduFiuF^vFcvFhvF]wFbwFg wF\\xFaxFfxFfx7$FgxF)F_dm-F-6&Fedm$\")+++]Fial$\"0+++++++#Fd[mFjdm-Fgc m6%7=7$$\"0m)f6I!p3(FcqF)FbemFfxFfxFayFfyF[zF`zFezFjzF_[lFd[lFi[lF^\\l Fc\\lFh\\lF]]lFb]lFg]lF\\^lFa^lFf^lF[_lF`_lFe_lFe_l7$Ff_lF)F_dmFcdm-Fg cm6%787$$\"0E'f " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 10 "Example 6 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "Let " }{XPPEDIT 18 0 "f(x)" "6#-%\"fG6#%\"xG" }{TEXT -1 51 " be the piecewise function defined on the interval " }{XPPEDIT 18 0 "[-2,2]" "6#7$,$\"\"#!\"\"F%" }{TEXT -1 4 " by " }}{PARA 257 "" 0 "" {TEXT -1 1 " " }{XPPEDIT 18 0 "f(x) = PIECEWISE([1-sqrt(-2*x-x^2) , -2 <= x and x < 0],[1-sqrt(2*x-x^2), 0 <= x and x <= 2])" "6#/-%\"fG 6#%\"xG-%*PIECEWISEG6$7$,&\"\"\"F--%%sqrtG6#,&*&\"\"#F-F'F-!\"\"*$F'F3 F4F431,$F3F4F'2F'\"\"!7$,&F-F--F/6#,&*&F3F-F'F-F-*$F'F3F4F431F:F'1F'F3 " }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 75 "This example illustrates the area of the region enclosed \+ between the graph " }{XPPEDIT 18 0 "y = f(x)" "6#/%\"yG-%\"fG6#%\"xG" }{TEXT -1 9 " and the " }{TEXT 290 1 "x" }{TEXT -1 32 " axis over the \+ interval [-2, 2]." }}{PARA 0 "" 0 "" {TEXT -1 26 "( Redraw with the op tion \"" }{TEXT 285 17 "areafunction=true" }{TEXT -1 50 "\" to obtain \+ an animation for the area function. ) " }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 179 "f := x -> piecewise(x<0 ,1-sqrt(-2*x-x^2),1-sqrt(2*x-x^2)):\n'f(x)'=f(x);\nareaplot(f(x),x=[-2 ..2,-2..2],areafunction=false,color=[brown$2,red],\n shading=ligh ten(neon_blue,.7));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"fG6#%\"xG- %*PIECEWISEG6$7$,&\"\"\"F-*$,&*&\"\"#F-F'F-!\"\"*$)F'F1F-F2#F-F1F22F' \"\"!7$,&F-F-*$,&*&F1F-F'F-F-F3F2F5F2%*otherwiseG" }}{PARA 13 "" 1 "" {GLPLOT2D 657 330 330 {PLOTDATA 2 "6/-%'CURVESG6$7%7$$!\"#\"\"!$\"\"\" F*F'F'-%'COLOURG6&%$RGBG$\"\"&!\"\"$\"$l\"!\"$F4-F$6$7!#<$\"3K\\$yU.5BE*!#=7$$!3SL$e9r]X*>F=$\"3!zU()*z1Yd*)F@7$$!35+v=ng #=*>F=$\"3u/vrDx-C()F@7$$!3#om;HU,\"*)>F=$\"3qZDw!>Uw_)F@7$$!3A+]PM@l$ )>F=$\"3GuI@.\"4#*>)F@7$$!3SLL$e%G?y>F=$\"3W!oo%pQ[BzF@7$$!3)****\\(oU In>F=$\"3yjh`oG\"QY(F@7$$!3ymmm\"p0k&>F=$\"33@ZT^kezqF@7$$!3&*****\\P& 3Y$>F=$\"3()3yI5%>KW'F@7$$!3MLLL$Q6G\">F=$\"3Z.!G.(e=;fF@7$$!31++v3-)[ (=F=$\"3e3$f:N1m:&F@7$$!3bmm;M!\\p$=F=$\"3'\\o0Jj\">FXF@7$$!3#)***\\7Y \"H%z\"F=$\"33>Kd%3JY#RF@7$$!3MLLL))Qj^/MF@7$$!3Z$e&=F@7$$!3OLL$3yO5]\"F=$\"3i,2^*4SdM\"F@7$$!3&*****\\nU)*=9 F=$\"3G1)Reo]1?*!#>7$$!3SLL$3WDTL\"F=$\"3QopA;&Qru&Fer7$$!35++]d(Q&\\7 F=$\"374csJ)=N;$Fer7$$!3gmmmc4`i6F=$\"3PV3m7blH8Fer7$$!3KLLLQW*e3\"F=$ \"3ELijwlv&p$!#?7$$!3qmm;arvU5F=$\"374@mhF0X\"*!#@7$$!0(************** !#:$\"\"#FdtF--F$6$7OFat7$$!3w++++()>'***F@$\"31@&\\?6T\\A(!#D7$$!3_++ ++Y0j&*F@$\"3;u.\"3&[i]&*F`t7$$!3E++++0\"*H\"*F@$\"331\"*z/,Z#z$Fjs7$$ !35++++83&H)F@$\"3q\"ft%4<4k9Fer7$$!3\\LLL3k(p`(F@$\"3E\"RIs/'p!3$Fer7 $$!3Anmmmj^NmF@$\"3B&\\I()Q3)HeFer7$$!3)zmmmYh=(eF@$\"3vpM/u$e%=*)Fer7 $$!3+,++v#\\N)\\F@$\"3A&*pQ[YE\\8F@7$$!3commmCC(>%F@$\"3Qpv*>I*zb=F@7$ $!39*****\\FRXL$F@$\"3AS1cB;OXDF@7$$!3V******\\0zBHF@$\"3*H8owcxS$HF@7 $$!3t*****\\#=/8DF@$\"31bh&f+j3P$F@7$$!3%HLL3ioW3#F@$\"3iPrwkl**))QF@7 $$!3=mmm;a*el\"F@$\"3-oT*Htk&)[%F@7$$!3_mm;H9Li7F@$\"3&oh%))*y\\l8&F@7 $$!3komm;Wn(o)Fer$\"3Q9m6wR;BfF@7$$!3sNL$3x9^c'Fer$\"3%>7(H!>.kV'F@7$$ !3$G++]7bDW%Fer$\"3[C\")**>:]_qF@7$$!3QOL3-`F\"Q$Fer$\"3%f#*[ao&e@uF@7 $$!3$*pm;za**>BFer$\"3cjZhkhYeyF@7$$!3[.+Dccre7Fer$\"3:A@'p=f$=%)F@7$$ !3IqLLL$eV(>Fjs$\"3g'RVF4A>P*F@7$$\"3O$fmTNc$\\!*Fjs$\"3KP?FYCtd')F@7$ $\"3qbm;/rI2?Fer$\"3C;7j))*Hk+)F@7$$\"31_m\"Hdy'4JFer$\"36I\"yG%)*fDvF @7$$\"3V[mmT+07UFer$\"37hMa`bHGrF@7$$\"3:Tm;zHz;kFer$\"3M(e?I#y`vkF@7$ $\"3)Qjmm\"f`@')Fer$\"3()H-Ho*4!QfF@7$$\"3mILLL1+Y7F@$\"3'39N.I1g;&F@7 $$\"3%z****\\nZ)H;F@$\"3*)*G!yGT?GXF@7$$\"3DJL$e*HTW?F@$\"3>%)**>F[BTR F@7$$\"3ckmm;$y*eCF@$\"3]Srfh(GCV$F@7$$\"3cJLLe[E()GF@$\"3goDo3l%3(HF@ 7$$\"3f)******R^bJ$F@$\"3q5[\\\")HQiDF@7$$\"3'e*****\\5a`TF@$\"3)fLKE4 9r)=F@7$$\"3'o****\\7RV'\\F@$\"3CO?92HVg8F@7$$\"3Y'*****\\@fkeF@$\"3g< w)eZS9&*)Fer7$$\"3_ILLL&4Nn'F@$\"35#z1UeI\\p&Fer7$$\"3A*******\\,s`(F@ $\"3e!f5l/C,3$Fer7$$\"3%[mm;zM)>$)F@$\"3iTa9T?e@9Fer7$$\"3M*******pfa< *F@$\"3e&\\],*480MFjs7$$\"3Ckm;zy*zd*F@$\"3QtR%=Nd#3*)F`t7$$\"39HLLeg` !)**F@$\"3G4h4?pA%*=!#B7$$\"0)**************Fdt$F*F*F--F$6$7=Fcbl7$$\" 3Lmm;W/8S5F=$\"3#*oq'\\I2b0)F`t7$$\"3w****\\#G2A3\"F=$\"39Z)=Q!pu%Q$Fj s7$$\"3;LLL$)G[k6F=$\"3]Kfh]i+i8Fer7$$\"3#)****\\7yh]7F=$\"3u9p(HA*Q\" >$Fer7$$\"3xmmm')fdL8F=$\"3%=(>$fWyws&Fer7$$\"3bmmm,FT=9F=$\"3MqnS\"=) Hu\"*Fer7$$\"3FLL$e#pa-:F=$\"3+nu.m1]a8F@7$$\"3!*******Rv&)z:F=$\"3#zX UG9@G&=F@7$$\"3ILLLGUYo;F=$\"3A#*H4cqbiDF@7$$\"3\"*****\\n'*33F=$\"32ntFQNQAfF@7$$\"31+]i0j\"[$>F=$\"3q6[V)p$ o[kF@7$$\"3/++v.Uac>F=$\"3i;F=$\"33t$o(H$yx Y(F@7$$\"3-+](=5s#y>F=$\"3b@j!y0\\n#zF@7$$\"39]iSwSq$)>F=$\"3lpb7k'[?? )F@7$$\"3-+v$40O\"*)>F=$\"3mq'4aJq*H&)F@7$$\"3%[7.#Q?&=*>F=$\"3'\\z?[5 [gs)F@7$$\"3!*\\(oa-oX*>F=$\"3M_0l3P6f*)F@7$$\"3%\\PMF,%G(*>F=$\"3)*)) Qo+8[j#*F@7$$FftF*F+FbjlF--F$6$7$FbjlFbjlF--%)POLYGONSG6%7@7$F(F*F'F'F :FAFFFKFPFUFZFinF^oFcoFhoF]pFbpFgpF\\qFaqFfqF[rF`rFfrF[sF`sFesF[tFatFa t7$FbtF*-%&STYLEG6#%,PATCHNOGRIDG-F.6&%$HSVG$\")nmmm!\")$\"0+++++S4#Fd t$\"0+++++++\"!#9-Fhjl6%7=7$Fe[lF*F\\[mFatFatFjtF`uFeuFjuF_vFdvFivF^wF cwFhwF]xFbxFgxF\\yFayFfyF[zF`zFezFjzF_[lFd[lFd[lF][mFa[m-Fhjl6%7 " 0 "" {MPLTEXT 1 0 1 ";" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "4 0 \+ 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }