I came across a rather frightening problem in my problem set and I am confused about it.
I need to compute the flux of a field $\vec F = \langle y, x^2, z(x^2-y^3)^7 \cos(e^{xyz}) \rangle$ through the upward-pointing surface $z= \sqrt {1 - \frac {x^2} 9 - \frac {y^2} 4} $.
I'm told it would be wise to use Stokes's Theorem and I'm also told to figure out the boundary to get a head start. I attempted to compute this integral with brute force, but it seems to be unintegrable that way.
How should I approach this problem?