Verfify Stokes' theorem for the given surface S and boundary ∂S, and vector fields F.
S = [(x,y,z): x2+y2+z2=1, z≥0
∂S = [(x,y): x2+y2=1
I did this problem and checked the answer - I chose the wrong integral bounds and I am wondering why they are wrong.
∫∫(∇×F)dS = ∫F⋅ds
The Attempt at a Solution
I was able to do the left hand of the solution easily. I knew that I should get zero for the cross product, so that's all I had to do.
For the right hand side:
∫F⋅dS = ∫xdx+ydy
Apparently this is the correct range for theta:
Why is it just π?