# Math Help - Area of inside a circle but outside a cardioid

1. ## Area of inside a circle but outside a cardioid

I need to find the area that is inside the circle with r=1 and outside the cardioid r = 1 + SIN THETA

I know the area of the later is 1/2 the integral of (1 + sin theta)^2 but I am having trouble with the bounds and how to deal with the circle. I would have thought it would be just pi times 1^2 times theta but.... the answer to this whole problem is 2 - pi/4 Can anyone lend a hand? THanks!

2. The area is $\int_{\pi}^{2\pi}\int_{1+\sin\theta}^1r\,drd\theta = \int_\pi^{2\pi}\left(\tfrac12-\tfrac12(1+\sin\theta)^2\right)d\theta$.