1.F(x,y,z)=
<z,x,y>, the box
[0,4]x[0,2]x[0,3]
IntInt(F.dS)(S)
=IntIntIntdiv(F)dV(R)
=IntIntInt0dV(R)=0
3.F(x,y,z)=[2x,3z,
3y],x^2+y^2<=1,
0<=z<=2 region div(T)
IntInt(F.dS)(S)
=IntIntIntdiv(F)
dV(R)=4pi
5.F(x,y,z)=
<0,0,z^3/3>,S
is the sphere x^2
+y^2+z^2=1->IntInt
(F.S)(S)->4pi/15
7.F(x,y,z)=[xy^2,
yz^2,zx^2],S=boundary
of cylinder illustrated
by x^2+y^2<=4,0<=z<=3->60pi
9.F(x,y,z)=<x+z^2,xz+y^2,
zx-y>,S->pc z=1-x^2
z=0,y-0,y+z=5->3616/105
11.F(x,y,z)=<x^3,0,z^3>
S->x^2+y^2+z^2<=4,x>=0,
y>=0,z>=0->32pi/5
15.F(x,y,z)=<x+y,z,z-x>
S=z=9-x^2-y^2 pc->81pi