Mathematics

Problem

The limaçon

r=1+2\cos\theta

has a small inner loop. What is the area enclosed by this inner loop? a)

2\pi-3\sqrt3

\sqrt3-\dfrac{\pi}{3}

\displaystyle \pi-\dfrac{3\sqrt3}{2}

\displaystyle \frac{\pi}{2}-\frac{3\sqrt3}{4}