How to find moment of inertia for a solid sphere by using only Cartesian Coordinates?
That depends with respect to which axis you want to calculate the moment of inertia, but I assume you mean an axis through the center of the sphere.
It can be done (ofcourse). The relatively hard part would be to find the boundaries of integration. It's silly to do it this way though, since in evaluating the integrals you'll likely make substitutions which result in the same sort of integrals you find when working in sphericla coordinates.
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