I've been given a question based on Stoke's Theorem, and the question is as follows:
Given the surface, and the vector field . Use stokes formula to evaluate the integral .
Using Stokes Theorem: .
So, I need to find . I can find a vector equation for S:
Then, I can calculate & . However, the latter leaves me with something that looks hideously ugly. I was just wondering if any could go over this, see whether I've done the right thing.
Thank you in advance!
Our surface is an ellipsoid of revolution about the z-axis, centred at (0,0,1). Setting z=0 we find our XY domain and it's the circle but since our condition was our domain becomes
We are evaluating at z=0 because we transformed our stokes equation into 2D which is only in the XY plain!
Transforming to polar co-ordinates