Let $\Phi$ denote gravitational potential. This is an example from a book (Classical dynamics, Thornton-Marion). We assume a homogeneous spherical shell. The writer says: We integrate over $d\phi$ in the expression for the potential. Thus
I don't follow this. It seems at first there is a coordinate transform at work, but then again we have two different functions being integrated over two different bounds - instead of a single composition map. And that's assuming this is an iterated integral, and not a product of two different integrals. Can someone explain the steps taken here? I can provide more information from the example if necessary.