The question asks to convert to spherical coordinates then evaluate.
So for this question, I manage to get the bounds of theta and row right, but I got the bounds of phi wrong. According to the solutions, it should be $0\leq \phi\leq \pi$, but through algebraic manipulation, I got $\pi/2$. (Basically what I did is I plugged in $x= \rho \sin \phi \cos \theta$, $y = \rho \sin \phi \sin \theta$ and $z = \rho \cos \phi$ to replace all the x y and z.) Can someone tell me why this is wrong and what approach should I take to find the bounds of phi?