I have to use the divergence theorem to calculate $$\int \int_C F.dS $$ for $$F = (x^2z^3, 2xyz^3,xz^4) $$ where S is the surface of the box with vertices at $(\pm1,\pm2,\pm3)$ with outward pointing normals.
I find that $div F = 8xz^3$, and the volume integral equals $0$. Is there something simple I'm forgetting to do?