I'm going to try this one as well. Since the polar graph goes around 2pi
then the inntegral from 0 to 2pi of (1/2+cosx)^2/2 -2*integral(2pi/3to4pi/3) (1/2+cosx)^2/2?
The 2* integral comes from the fact that you have to subtract the inner loop twice since it went around twice initially.
Verify anyone?