I'm given two spheres; $x^2+y^2+z^2=1$ and $x^2+y^2+z^2=2$. I'm trying to convert from rectangular to spherical coordinates to integrate the region between the two spheres, and my bounds so far are $1\leqslant p \leqslant 2$, $0\leqslant \theta \leqslant 2\pi$, and $0\leqslant\phi\leqslant \pi/2$. When I plug these in and integrate I'm getting the wrong answer, and I checked that my integration was correct so it must be an issue with the bounds.
Any help is appreciated.