Compute the double integral of the curl of F over the surface S, where S is the union of S1, the set of (x,y,z) with x^2+y^2=1, z:[0,1], and S2, the set of (x,y,z) with x^2+y^2+(z-1)^2=1, z is greater than or equal to 1. F(x,y,z)=(xz+yz^2+x)i+(xyz^3+y)j+((x^2)*(z^4))k.

I know that I can use Stokes theorem and solve for the line integral of F around the boundary of S. I think the boundary will be parametrized by the curve c(t)=cos(t)i+sin(t)j, but then how do I define z?

Question

Compute the double integral of the curl of F over the surface S, where S is the union of S1, the set of (x,y,z) with x^2+y^2=1, z:[0,1], and S2, the set of (x,y,z) with x^2+y^2+(z-1)^2=1, z is greater than or equal to 1. F(x,y,z)=(xz+yz^2+x)i+(xyz^3+y)j+((x^2)*(z^4))k.

I know that I can use Stokes theorem and solve for the line integral of F around the boundary of S. I think the boundary will be parametrized by the curve c(t)=cos(t)i+sin(t)j, but then how do I define z?

anonymous · Answer

is z=0?