Trying to find the moment of inertia about a diameter of a spherical shell of uniform density, D, bounded by two concentric spheres of radii a and b, where a<b. Should express answer in terms of a, b, and the mass M of the spherical shell.

Could somebody check my answer? Or suggest a way for me to double check it?

$\displaystyle

6/5 (b^5-a^5)/(b^3-a^3)M$