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{SECT 0 {SECT 0 {PARA 3 "" 0 "" {TEXT -1 14 "Line Integrals" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 257 12 "Description:" }{TEXT -1 
55 " Line integrals with respect to arclength, dx, and dy (" }{TEXT 
260 9 "animation" }{TEXT -1 1 ")" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 
4 "Code" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "with(plottools):
\nwith(plots):" }}{PARA 7 "" 1 "" {TEXT -1 43 "Warning, the name arrow
 has been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 43 "Warning, the nam
e arrow has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 79 "f:=(x,y)->(x^2+2*y^2+1)/25:\nx:=t->3*t+0.3*(t+cos(5*t)):\ny:=t->
t^2+0.3*sin(4*t):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 604 "curva:=spacec
urve([x(t),y(t),0],t=0..3,color=red,thickness=2):\ncurvb:=spacecurve([
x(t),y(t),f(x(t),y(t))],t=0..3,color=red,thickness=2):\ncurvx:=spacecu
rve([x(t),0,f(x(t),y(t))],t=0..3,color=orange,thickness=2):\ncurvy:=sp
acecurve([0,y(t),f(x(t),y(t))],t=0..3,color=orange,thickness=2):\nplot
f:=plot3d(f(x,y),x=0..10,y=0..10,style=wireframe,color=blue):\nrack:=p
lot3d([x(t),y(t),s*f(x(t),y(t))],t=0..3,s=0..1,color=coral,style=patch
nogrid):\nxrack:=plot3d([x(t),0,s*f(x(t),y(t))],t=0..3,s=0..1,color=gr
een,style=patchnogrid):\nyrack:=plot3d([0,y(t),s*f(x(t),y(t))],t=0..3,
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:\nframe[2]:=display([plotf,curva],axes=boxed,labels=[`x`,`y`,`z`],sca
ling=constrained,orientation=[20,45],title=`Curve C on the xy-plane`):
\nframe[3]:=display([plotf,curva,curvb],axes=boxed,labels=[`x`,`y`,`z`
],scaling=constrained,orientation=[20,45],title=`Curve C on the xy-pla
ne and its lift on the graph of f(x,y)`):\nframe[4]:=display([plotf,cu
rva,curvb,rack],axes=boxed,labels=[`x`,`y`,`z`],scaling=constrained,or
ientation=[20,45],title=`Area representing the line integral of f(x,y)
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rva,curvb,rack,curvx,xrack],axes=boxed,labels=[`x`,`y`,`z`],scaling=co
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splay([plotf,curva,curvb,rack,curvx,xrack,curvy,yrack],axes=boxed,labe
ls=[`x`,`y`,`z`],scaling=constrained,orientation=[20,45],title=`Area r
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