I am not understanding integration with polar coordinates, or at least visualizing what is happening. Here's the integral calculated in Wolfram:
http://www.wolframalpha.com/input/?i=integrate+%28r%5E2%28cost%5E2-sint%5E2%29%29r+drdt+t%3D%280%29..%28pi%2F2%29+r%3D%281%29..%282%29+
the...