# Gauss's Theorem problem

1. Nov 26, 2005

Verify the divergence theorem by evaluating both the surface and the volume integrals for the region bounded by $$x^2+y^2=a^2$$ and $$z=h$$ for the vector field:

$$\mathbf{F}=(x,y,z)$$

For the volume integral, it's easy. Since divF =3, it's just $$3\pi a^2h$$. However, for the surface integral, I divided it into 3 parts. The top and bottom discs, and the side of the cylinder. It's the side that I'm having trouble with:

$$F*N=\sqrt{x^2+y^2}$$, but how should the parameters vary?

2. Nov 26, 2005