Análisis Matemático IV
Problemas de integrales dobles y triples
I. Marrero
Curso 2007/08
| > | restart: |
| > | with(plots): |
| > | read "calcplot2.txt"; |
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Integrales dobles - Problema 13
| > | f:=x*y;
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(1.1) |
| > | domy:=y=0..2;
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(1.2) |
| > | domx:=x=y-2..3*sqrt(4-y^2)/2;
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(1.3) |
| > | Int( Int(f, domx), domy) = int( int( f, domx), domy);
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(1.4) |
| > | Dxy := dxdyplot( domx, domy ): display(Dxy, axes=normal,labels=[`eje x`,`eje y`],tickmarks=[3,3]);
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Integrales dobles - Problema 20
(a)
| > | f:=r*(1+r^2)^(-3/2);
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(2.1.1) |
| > | domr:=r=0..1/cos(theta);
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(2.1.2) |
| > | domt:=theta=0..Pi/4;
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(2.1.3) |
| > | Int( Int(f, domr), domt) = int( int(f, domr), domt);
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(2.1.4) |
| > | Drt := drdtplot( domr, domt ): display(Drt, axes=normal,labels=[`eje x`,`eje y`],tickmarks=[3,3]);
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(b)
| > | f:=r^4*(cos(theta)^3+sin(theta)^3);
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(2.2.1) |
| > | domr:=r=2*cos(theta)..1;
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(2.2.2) |
| > | domt:=theta=Pi/3..Pi/2;
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(2.2.3) |
| > | Int( Int(f, domr), domt) = int( int(f, domr), domt);
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(2.2.4) |
| > | Drt := drdtplot( domr, domt ): display(Drt, axes=normal,labels=[`eje x`,`eje y`],tickmarks=[3,3]);
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Integrales triples - Problema 11
| > | f:=1-x-y-z;
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(3.1) |
| > | domz:=z=0..1-x-y;
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(3.2) |
| > | domy:=y=0..1-x;
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(3.3) |
| > | domx:=x=0..1;
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(3.4) |
| > | Int( Int( Int(f, domz), domy), domx) = int( int( int(f, domz), domy), domx);
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(3.5) |
| > | Dzyx := dzdydxplot( domz, domy, domx ): display(Dzyx, axes=normal,labels=[`eje x`,`eje y`,`eje z`],tickmarks=[3,3,3]);
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Integrales triples - Problema 16
(a)
| > | f:=r^5;
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(4.1.1) |
| > | domz:=z=r^2/2..2;
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(4.1.2) |
| > | domr:=r=0..2;
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(4.1.3) |
| > | domt:=theta=0..2*Pi;
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(4.1.4) |
| > | Int( Int( Int(f, domz), domr), domt) = int( int( int(f, domz), domr), domt);
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(4.1.5) |
| > | Dzrt := dzdrdtplot( domz, domr, domt ): display(Dzrt, axes=normal,labels=[`eje y`,`eje x`,`eje z`],tickmarks=[3,3,3],orientation=[39,72]);
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(b)
| > | f:=z*exp(-r^2)*r;
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(4.2.1) |
| > | domz:=z=sqrt(2)*r..sqrt(r^2+1);
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(4.2.2) |
| > | domr:=r=0..1;
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(4.2.3) |
| > | domt:=theta=0..2*Pi;
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(4.2.4) |
| > | Int( Int( Int(f, domz), domr), domt) = int( int( int(f, domz), domr), domt);
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(4.2.5) |
| > | Dzrt := dzdrdtplot( domz, domr, domt ): display(Dzrt, axes=normal,labels=[`eje y`,`eje x`,`eje z`],tickmarks=[3,3,3],orientation=[39,63]);
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Integrales triples - Problema 20
(a)
| > | f:=rho^5*sin(phi)^3*cos(phi)*cos(theta)*sin(theta);
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(5.1.1) |
| > | domp:=rho=0..1;
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(5.1.2) |
| > | domphi:=phi=0..Pi/2;
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(5.1.3) |
| > | domt:=theta=0..Pi/2;
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(5.1.4) |
| > | Int( Int( Int(f, domp), domphi), domt)= int( int( int(f, domp), domphi), domt);
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(5.1.5) |
| > | Drpt := dpdphidtplot( domp, domphi, domt ): display(Drpt, axes=normal,labels=[`eje x`,`eje y`,`eje z`],tickmarks=[3,3,3],orientation=[-24,57]);
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(b)
| > | a:='a';
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(5.2.1) |
| > | f:=rho^4*sin(phi);
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(5.2.2) |
| > | domp1:=rho=2*a*cos(phi)/sin(phi)^2..sqrt(3)*a;
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(5.2.3) |
| > | domphi1:=phi=arccos(1/sqrt(3))..Pi/2;
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(5.2.4) |
| > | domt1:=theta=0..2*Pi;
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(5.2.5) |
| > | domp2:=rho=0..sqrt(3)*a;
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(5.2.6) |
| > | domphi2:=phi=Pi/2..Pi;
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(5.2.7) |
| > | domt2:=theta=0..2*Pi;
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(5.2.8) |
| > | Int( Int( Int(f, domp1), domphi1), domt1)+Int( Int( Int(f, domp2), domphi2), domt2)=int( int( int(f, domp1), domphi1), domt1)+int( int( int(f, domp2), domphi2), domt2);
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(5.2.9) |
| > | a:=4;
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(5.2.10) |
| > | Drpt1 := dpdphidtplot( domp1, domphi1, domt1 ):
Drpt2 := dpdphidtplot( domp2, domphi2, domt2 ): display({Drpt1,Drpt2}, axes=normal,labels=[`eje y`,`eje x`,`eje z`],tickmarks=[3,3,3]); |
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