The limaçon has a small inner loop

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

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

(b)

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

(c)

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

(d)

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