1. The problem statement, all variables and given/known data Hello PF! I'm having some trouble on the last part of my assignment, it's question 4 part "c". Here is a picture of the assignment [http://imgur.com/1edJ3g5] ! I'll post this instead of writing it out so we know that we're all looking at the same thing! 2. Relevant equations The change of variables given at the beginning of question 4 are, x=au, y=bv, z=cw From part "a" I used the change of variables given in the question and found that the ellipsoid equation became u^2 + v^2 + w^2 = 1. I found the Jacobian to be equal to abc. Next I set up my integral to determine the volume over the region S, ∫∫∫abc dV, Since a sphere with the radius 1 will have a volume of 4pi/3 I found my volume to be abc*4pi/3. I think what I need for part "c" is just the Jacobian. so the Jacobian = abc. The equation for inertia that we were given in class was I=∫∫(x^2 + y^2)*ρ(x,y) dA Changing from rectangular to spherical coordinates. (I think you need to use this)* x = ρsin(β)cosΘ y=ρsin(β)sinΘ z=ρcos(β) 3. The attempt at a solution So to start off since I'm working in 3 Dimensions would I have to change my formula for moment of inertia to, I=∫∫∫(x^2 + y^2 + z^2)*ρ(x,y,z) dV, Then from here since I am working with changed variables I changed the x, y, and z, also multiplied by the Jacobian, I=∫∫∫((au)^2 + (bv)^2 + (cw)^2)*ρ(x,y,z)*abc dV From here would I have to switch to spherical coordinates? I would obtain, I=∫∫∫((ρsin(β)cosΘ)^2 + (ρsin(β)sinΘ)^2 + (ρcos(β))^2)*ρ(ρ,Θ,β)*abc dV I=∫∫∫(ρ^2)*ρ(ρ,Θ,β)*abc*(ρ^2)sin(β) dρdΘdβ Then my bounds of integration would be 0 ≤ ρ ≤ 1 0 ≤ Θ ≤ 2pi 0 ≤ β ≤ pi Does this look right so far, Or am I off track? if it looks good just let me know and I will continue, I'll reply as soon as I have either finished or got stumped again!