You're having trouble converting the integrand into cylindrical coordinates? What happens when you plug in for x and y?
No, I don't think you've quite got it yet. Just plugging in gives:
You see how I work here: step-by-step. I don't often skip steps.
The other thing you have to worry about is that the volume differential in cylindrical components is not just
So, putting this all together, what does your integral look like now?