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" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 257 12 "Description:" }{TEXT -1 38 " Changing the order of integ ration in " }{XPPEDIT 18 0 "int(int(int(f(x,y,z),y = 0 .. 1-x),z = 0 . . 1-x^2),x = 0 .. 1)" "6#-%$intG6$-F$6$-F$6$-%\"fG6%%\"xG%\"yG%\"zG/F. ;\"\"!,&\"\"\"F4F-!\"\"/F/;F2,&F4F4*$F-\"\"#F5/F-;F2F4" }{TEXT -1 2 " \+ (" }{TEXT 260 9 "animation" }{TEXT -1 2 ")." }}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 4 "Code" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "with(p lottools):\nwith(plots):" }}{PARA 7 "" 1 "" {TEXT -1 62 "Warning, the \+ names arrow and changecoords have been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 584 "c1:=spacecurve([x,0,0],x=0..1,thickness=2, color=red):\nc2:=spacecurve([0,0,z],z=0..1,thickness=2,color=red):\nc3 :=spacecurve([x,0,1-x^2],x=0..1,thickness=2,color=red):\nc4:=spacecurv e([0,y,0],y=0..1,thickness=2,color=red):\nc5:=spacecurve([x,1-x,0],x=0 ..1,thickness=2,color=red):\nc6:=spacecurve([0,y,1],y=0..1,thickness=2 ,color=red):\nc7:=spacecurve([0,1,z],z=0..1,thickness=2,color=red):\nc 8:=spacecurve([x,1-x,1-x^2],x=0..1,thickness=2,color=red):\nplane:=plo t3d([x,1-x,z],x=0..1,z=0..1,color=yellow,style=patchnogrid):\ncyl:=plo t3d([x,y,1-x^2],x=0..1,y=0..1,color=blue,style=patchnogrid):\n" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 377 "volume:=display([plot3d([x,1-x,z], x=0..1,z=0..1-x^2,color=yellow,style=patchnogrid),\nplot3d([x,y,1-x^2] ,x=0..1,y=0..1-x,color=blue,style=patchnogrid),\nplot3d([x,0,z],x=0..1 ,z=0..1-x^2,color=violet,style=wireframe,grid=[10,10]),\nplot3d([x,y,0 ],x=0..1,y=0..1-x,color=violet,style=wireframe,grid=[10,10]),\nplot3d( [0,y,z],y=0..1,z=0..1,color=violet,style=wireframe,grid=[10,10])]):" } {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 618 "frame[1]:=display( \{c1,c2,c3,c4,c5\},scaling=constrained,axes=boxed):\nframe[2]:=display (\{frame[1],cyl,plane\},scaling=constrained,axes=boxed):\nframe[3]:=di splay(\{frame[2],c6,c7,c8\},scaling=constrained,axes=boxed):\nframe[4] :=display(\{c1,c2,c3,c4,c5,c6,c7,c8,volume\},scaling=constrained,axes= boxed):\nframe[5]:=display(frame[4],scaling=constrained,axes=boxed,ori entation=[-110,60]):\nframe[6]:=display(frame[4],scaling=constrained,a xes=boxed,orientation=[-90,90]):\nframe[7]:=display(frame[4],scaling=c onstrained,axes=boxed,orientation=[-90,0]):\nframe[8]:=display(frame[4 ],scaling=constrained,axes=boxed,orientation=[180,90]):" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 5 "Plots" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 163 "display([seq(frame[i],i=1.. 8)],scaling=constrained,axes=boxed,labels=[`x`,`y`,`z`],insequence=tru e,title=`int(int(int(f(x,y,z),y=0..1-x),z=0..1-x^2),x = 0 .. 1)`);" }} {PARA 13 "" 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "6'-%(ANIMATEG6*7)- %'CURVESG6%7T7%$\"\"!F-F,F,7%$\"+Ej\"3/#!#6F,F,7%$\"+_Ej\"3%F1F,F,7%$ \"+y*[C7'F1F,F,7%$\"+/`Ej\")F1F,F,7%$\"+j\"3/-\"!#5F,F,7%$\"+'z*[C7F>F ,F,7%$\"+H9dG9F>F,F,7%$\"+iIlK;F>F,F,7%$\"+&pMn$=F>F,F,7%$\"+Gj\"3/#F> F,F,7%$\"+hz*[C#F>F,F,7%$\"+%fz*[CF>F,F,7%$\"+F71`EF>F,F,7%$\"+gG9dGF> F,F,7%$\"+$\\C71$F>F,F,7%$\"+EhIlKF>F,F,7%$\"+fxQpMF>F,F,7%$\"+#RpMn$F >F,F,7%$\"+D5bxQF>F,F,7%$\"+eEj\"3%F>F,F,7%$\"+\"H9dG%F>F,F,7%$\"+Cfz* [%F>F,F,7%$\"+dv(Qp%F>F,F,7%$\"+!>fz*[F>F,F,7%$\"+B3/-^F>F,F,7%$\"+cC7 1`F>F,F,7%$\"+*3/-^&F>F,F,7%$\"+AdG9dF>F,F,7%$\"+btO=fF>F,F,7%$\"+))*[ C7'F>F,F,7%$\"+@1`EjF>F,F,7%$\"+aAhIlF>F,F,7%$\"+()QpMnF>F,F,7%$\"+?bx QpF>F,F,7%$\"+`r&G9(F>F,F,7%$\"+'yQpM(F>F,F,7%$\"+>/-^vF>F,F,7%$\"+_?5 bxF>F,F,7%$\"+&o$=fzF>F,F,7%$\"+=`Ej\")F>F,F,7%$\"+^pMn$)F>F,F,7%$\"+% eG9d)F>F,F,7%$\"+<-^v()F>F,F,7%$\"+]=fz*)F>F,F,7%$\"+$[tO=*F>F,F,7%$\" +;^v(Q*F>F,F,7%$\"+\\n$=f*F>F,F,7%$\"+#Q=fz*F>F,F,7%$\"+,+++5!\"*F,F,- %'COLOURG6&%$RGBG$\"*++++\"!\")F,F,-%*THICKNESSG6#\"\"#-F(6%7TF+7%F,F, F/7%F,F,F37%F,F,F67%F,F,F97%F,F,F<7%F,F,F@7%F,F,FC7%F,F,FF7%F,F,FI7%F, F,FL7%F,F,FO7%F,F,FR7%F,F,FU7%F,F,FX7%F,F,Fen7%F,F,Fhn7%F,F,F[o7%F,F,F ^o7%F,F,Fao7%F,F,Fdo7%F,F,Fgo7%F,F,Fjo7%F,F,F]p7%F,F,F`p7%F,F,Fcp7%F,F ,Ffp7%F,F,Fip7%F,F,F\\q7%F,F,F_q7%F,F,Fbq7%F,F,Feq7%F,F,Fhq7%F,F,F[r7% F,F,F^r7%F,F,Far7%F,F,Fdr7%F,F,Fgr7%F,F,Fjr7%F,F,F]s7%F,F,F`s7%F,F,Fcs 7%F,F,Ffs7%F,F,Fis7%F,F,F\\t7%F,F,F_t7%F,F,Fbt7%F,F,Fet7%F,F,Fht7%F,F, F[uF^uFeu-F(6%7T7%F,$\"\"\"F-F,7%F/$\"+n$=fz*F>F,7%F3$\"+Nn$=f*F>F,7%F 6$\"+-^v(Q*F>F,7%F9$\"+qMn$=*F>F,7%F<$\"+P=fz*)F>F,7%F@$\"+/-^v()F>F,7 %FC$\"+r&G9d)F>F,7%FF$\"+QpMn$)F>F,7%FI$\"+0`Ej\")F>F,7%FL$\"+sO=fzF>F ,7%FO$\"+R?5bxF>F,7%FR$\"+1/-^vF>F,7%FU$\"+t(QpM(F>F,7%FX$\"+Sr&G9(F>F ,7%Fen$\"+2bxQpF>F,7%Fhn$\"+uQpMnF>F,7%F[o$\"+TAhIlF>F,7%F^o$\"+31`EjF >F,7%Fao$\"+v*[C7'F>F,7%Fdo$\"+UtO=fF>F,7%Fgo$\"+4dG9dF>F,7%Fjo$\"+wS? 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