I have a question on whether I can do this with an integral:
When I tried solving this, I got (1/2)(M^2)(R^2) instead of (1/2)MR^2
Problem: https://i.stack.imgur.com/wZNbY.jpg
*Sorry for lack of TeX. Currently on iPad.
2026-03-31 17:57:03.1774979823
Proving the moment of inertia formula for right cylinder
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$p(x,y,z)$ doesn't pull out of the integral and turn into an $M$. It depends on $x,y,z$, you need to actually integrate it. What you wrote says that $\int fg=\int f \int g$ which is not true in general.