How to Calculate Moment of Inertia for a Disk Using Calculus?

[jeremy5561]

I know that the moment of inertia of a disk about the axis perpendicular to the plane of the disk is

I=1/2 MR^2

and by the perpendicular axis theorem the moment of inertia about the other axis is

I=1/4 MR^2

I want to get the 2nd result with calculus. I can't get the right answer. What am I doing wrong?

I know the moment of inertia of a rod is 1/12 MR^2
I take the mass of a section of the disc to me pyr dx where y is the depth of the disc
but when I integrate it gets really messy.

What's the correct way to do this?

http://individual.utoronto.ca/jeremyli/moi.jpg

 

[jeremy5561]

I got it

OH nevermind I got it.