I need to compute an integral that will represent the area outside of $r = 2$ but inside $r = 4\cos(\theta)$, both of which are polar equations.
After finding the intersection points to be $(1/3)\pi$ and $(5/3)\pi$, how do I set up the integral next?
Note that the two curves intersect at $\pm\frac\pi3$. So, the area is
$$\int_{-\pi/3}^{\pi/3} \int_2^{4\cos\theta }rdrd\theta =2\sqrt3+\frac{4\pi}3 $$