1. The problem statement, all variables and given/known data I need to know how to derive the equation for the moment of inertia of a rectangle rotated about an axis through its center. The rectangle has sides a and b. I know the equation to be (1/12)M(a2+b2), but I am having trouble deriving it. I have searched all over the internet without finding any helpful solutions. 2. Relevant equations dI = ∫r2dm dm = λdA 3. The attempt at a solution I started by taking a point mass of the rectangle to be the distance r from the center. This point would have the mass dm. dm would then equal λdA λ would equal M/A or M/ab dA would be the area of the small point. I'm guessing this would be dydx So, for dm we have (M/ab)(dydx) Now for r2. By pythagorean thereom, r2 = x2+y2. Substituting these into the equation ∫r2dm, we have (M/ab)∫(x2+y2)dydx I'm pretty sure this is incorrect, but even if it is correct I have no idea how to integrate it. I don't even know what limits to integrate about.