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For questions about problems related to physics that involve evaluating integrals. Purely mathematical questions should be asked at math.SE.
2
votes
Accepted
Center-of-mass and relative coordinate integral transformation
It looks like you have a pair of 3D integration variables in spherical coordinates, albeit ones in which you've integrated out the angular coordinates. …
11
votes
Why doesn't this way of calculating the moment of inertia of a sphere work?
That's a good, well-stated question and the premise is indeed correct: your independent approach has failed. It fails because you're using $r$ for the distance of the mass of a spherical shell of radi …