here's a particular question I'm working on that the textbook doesn't have the same answer as me.
Use The Divergence Theorem for: $F = |r|r$, where $r = <x,y,z>$, and $S$ consists of the hemisphere $z=\sqrt{1-x^2-y^2}$ and the disk $x^2 + y^2 \leq 1$
Here's what I have using spherical coordinates:
$|r| = p$
$\nabla \times r = 3$
Multiplying them both together we get: $3p$
Using spherical coordinates we get:
$\int_{0}^{\frac{\pi}{2}} \int_{0}^{2\pi} \int_{0}^{1} 3p^3sin\phi$ $dp d\phi d\theta$
Integrating gives us: $\frac{3\pi}{2}$ but the answer in the textbook is $2\pi$, I integrated it correctly, so that means that I either didn't set the question up properly, or the textbook answer key is wrong.
Anyway, thanks.