> #sfb 0ct24, 2002
> with(plots);
> Int(Int(Int(f,y=0..sqrt(1-z^2)),z=-1..1),x=0..1);
> Int(Int(Int(f,y=0..sqrt(1-x^2-z^2)),x=-sqrt(1-z^2)..sqrt(1-z^2)),z=0..1);
> Int(Int(Int(f,x=-sqrt(1-y^2-z^2)..sqrt(1-y^2-z^2)),y=-sqrt(1-z^2)..sqrt(1-z^2)),z=0..1);
> Int(Int(r^2*cos(theta),r=0..1),theta=Pi/2..3*Pi/2);int(int(r^2*cos(theta),r=0..1),theta=Pi/2..3*Pi/2);
> int(int(r^3*sin(theta)*cos(theta),r=0..2),theta=0..Pi/4);
> 
> 
> 
> 
> 
> 
> 
> # From last time
> with(linalg):with(plottools):
> F:=[x,0];
> A:=fieldplot(F,x=-2..2,y=0..2,arrows=thick,grid=[7,7]):A;
> B:=plot([cos(t),sin(t),t=0..Pi],color=blue):B;
> display(A,B,scaling=constrained);
> #C:=plot3d([cos(t),sin(t),s*(-sin(t)*cos(t))],t=0..Pi,s=0..1):C;
> C:=plot3d([cos(t),sin(t),s*(-sin(t)*cos(t))],t=0..Pi,s=0..1):C;
> display3d(A,B,C,scaling=constrained);
> with(plottools);
> T:=transform((x,y)->[x,y,0]):
> display(T(A),T(B),C);
> #
> r:=vector([cos(t),sin(t)]);
> diff(r,t);map(diff,r,t);
> r:=[cos(t),sin(t)];r[1];
> diff(r,t);
> map(diff,r,t);
> F:=vector([x,0]);
> fieldplot(F,x=-3..3,y=-3..3);
> 
> eval(F,{x=r[1],y=r[2]});eval(subs({x=r[1],y=r[2]},F));
> pretty:=subs({x=r[1],y=r[2]},dotprod(F,diff(r,t),orthogonal));
> int(pretty,t=0..2*Pi);
> #machine
> r:=[0,cos(t),sin(t)];a:=0;b:=2*Pi;F:=[-z/sqrt(x^2+z^2),y/sqrt(x^2+z^2),x/sqrt(x^2+z^2)];
> v:=diff(r,t);Ft:=subs({x=r[1],y=r[2],z=r[3]},F);inside:=dotprod(Ft,v,orthogonal);
> Int(inside,t=a..b)=int(inside,t=a..b);
> display(fieldplot(F,x=-2..2,y=-2..2),circle(),scaling=constrained);
>