Formula for area in a special occasion in polar coordinates.

Question

I know that the area of a curve given in polar coordinates is $$\int_{\theta_1}^{\theta_2}\frac{r^2}{2}d\theta$$. But what is the area outside one curve and inside another, when one of them is not entirely inside the other? For example, what is the area inside $a(1+\cos{\theta})$ and outside $a\sin{\theta}$?

Answer 1

integrate the cardioid from $-\pi$ to $\frac {\pi}{2}$ and subtract half the circle