Hi all,
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 .
My answer:
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!
Are you using "Calculus: A complete Course" by Robert A Adams? This is a question directly from the text.
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
Noting that,
We get,
We are evaluating at z=0 because we transformed our stokes equation into 2D which is only in the XY plain!
Thus,
Transforming to polar co-ordinates