A thin ring has inner radius 1m, outer radius 3m, and has density directly proportional to the distance from the centre of the ring. In polar coordinates, set up but do not evaluate the double iterated integral to find the moment of intertia about a line tangent to the outside of the ring.

I'm just curious whether I've done this one correctly or not. I've chosen my origin at the centre of the ring and the line tangent to the outside of the ring to be x = 3.

Does anyone see any problems?