Hello. I am attempting to derive the equation for the moment of inertia of a filled sphere. I do not how how to do the proper notation by typing, so I have attached a scan of my work(I apologize if opening the attachment is inconvenient)(adsbygoogle = window.adsbygoogle || []).push({});

I keep getting the correct order final equation, but my coefficient is 3/5 instead of 2/5. I am trying to do this using only single-variable calculus, so please do not use double integrals, etc unless you think they can be explained to a high schooler. If it is actually impossible to solve this problem using only one-variable integration, please tell me so and explain why. Thank you very much.

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# Moment of Inertia for a Filled Sphere

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