The surface density of a thin rectangle varies as:

Question

σ(x,y)= 14.0 kg/m2 + 9.00 kg/m4(x2+y2)
The rectangle has a length L = 0.500 m and a width W = 1.500 m. Calculate Iz, the moment of inertia about the z-axis.

Answer 1

I tried this but got a major mess.

x^2+y^2 = r^2 luckily

I = integral r^2(14+9r^2)(2 pi r dr)

but the limits are a serious mess and I was unable to figure it out, sorry

Answer 2

Oh, perpendicular axis theorem might help:
http://hyperphysics.phy-astr.gsu.edu/hbase/perpx.html