Verify the divergence theorem by computing both integrals for the vector field
F = <x^3, y^3, z^2> over a cylindrical region define by x^2+y^2 ≤ 9.
Divergence Theorem, and Flux Integrals.
The Attempt at a Solution
I did the divergence theorem, and got 279 pi for my answer. I did the integral in cylindrical, and regular with the same answer so that I know is correct. I know I need to break this up into three different surfaces. I can do the top, and the bottom easily since N = <0, 0, 1> for the top, and N = < 0, 0, -1> for the bottom, then I just plug in the z value for it.
The side of the cylinder is giving me trouble. I have looked up ways to do it online, but they make no sense, or are disorganized. Where do I start, and then where do I go from there?