This is certainly not my favorite calculus topic.

$\displaystyle \int_{-7}^7\int_{-\sqrt{49-y^2}}^{\sqrt{49-y^2}}\int_{-\sqrt{49-x^2-y^2}}^{\sqrt{49-x^2-y^2}} (x^2z+y^2z+z^3)dzdxdy$

I am to solve this by converting to spherical coordinates.

I guessed the region of integration was the volume of the sphere $\displaystyle x^2+y^2+z^2=49$.

So I had:

$\displaystyle \int_0^{2\pi}\int_0^{\pi}\int_0^7{\rho}^5cos{\phi} sin{\phi}d{\rho}d{\theta}d{\phi}$

Went about solving, and..ended up with 0.