For a planar object which lies in the x − y plane, Ix = ∫ x^2dm and Iy = ∫ y^2dm and according to perpendicular axis theorem , Iz = ∫ (x^2 + y^2)dm = ∫ r^2dm is the rotational inertia around the z axis and r is the distance from the z axis.
In that case r changes from 0 to a and since the disk...