1. The problem statement, all variables and given/known data Let R be the solid region that is bounded by two spheres x^2 + y^2 + z^2=1 and x^2 + y^2 + z^2=2. Determine the moment of inertia of R around the x-axis if the mass density per unit volume of R is u=sqrt(x^2 + y^2 + z^2). 2. Relevant equations Moment of Inertia around the x-axis: triple integral (y^2+z^2)*u(x,y,z) dxdydz using (p,@,theta) for spherical coordinates as it will be faster to type, sorry for any confusion. spherical coordinates: x=psin(@)cos(theta) y=psin(@)sin(theta) z=pcos(@) 3. The attempt at a solution Using the Moment of Inertia around the x-axis equation, i first got the equation: triple integral (y^2+z^2)*sqrt(x^2 + y^2 + z^2) dxdydz now converting to spherical coordinates i got: triple intergal (p^2*sin^2(@)*sin^2(theta) + p^2*cos^2(@))*sqrt(p^2*sin^2(@)*cos^2(theta) + p^2*sin^2(@)*sin^2(theta) + p^2*cos^2(@)) dpd@dtheta After some simplification: triple intergal p^3(sin^2(@)sin^2(theta) + cos^2(@)) dpd@dtheta where 1<p<sqrt(2) and 0<@<pi and 0<theta<2pi the 1<p<sqrt(2) is because of the two radius and the other two because its a sphere and its centred at the origin, i know 0<theta<2pi is correct but i'm not sure if 0<@<pi or 0<@<2pi. solving this integral i got 9*pi^2/4 which i'm not sure is correct as i'm not sure if i'm even able to do it this way, any tips or help would be much appreciated !