Subject: Calculate Inertia of a partially hollow sphere

Density is proportional to 1/r, from R1 to R2: the center of the sphere is 
hollow.  Using thin sphere Inertia formula I=2/3MR^2:  My dilema exist in 
when to integrate the proportional density// one way I end up with: 
I=1/3M(R2^2 + R1^2)  the other way I end up with:  I=2/3M(R2^2 + R1^2)  
any help would be appreciated.

Re: Calculate Inertia of a partially hollow sphere