Mathematics

Problem

The circle

r=2

and the limaçon

r=4\cos\theta

intersect at

\theta=\pm\tfrac{\pi}{3}

. Determine the exact area of the region that lies inside

r=4\cos\theta

and outside

r=2

. a)

\displaystyle \frac{8\pi}{3}+4\sqrt{3}

\displaystyle \frac{2\pi}{3}+\sqrt{3}

\displaystyle \frac{4\pi}{3}+2\sqrt{3}

\displaystyle \frac{4\pi}{3}-2\sqrt{3}