I'm stuck on this problem,
Consider the domain in the u - v plane bounded by the circle u^2+v^2=1 and the surface S in R^3 defined parametrically by
r(u,v)=(u^2+v^2)i + (uv)j + (u+v)k
where the positive sense around the boundary is determined by the positive sense around the boundary of the region in the u - v plane.
Set F= (yz)i + (xz)j + (xy)k
Compute SS(curlF).n dS. It is a double integral where . is the dot product between the curlF and the normal n.
I've done problems similar to this, but never with different variables as the boundary. How do I set this up as an integral?