Consider the region that lies inside the curve and outside the curve for

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

Problem

Consider the region that lies inside the curve

r_1(\theta)=3\cos\theta

and outside the curve

r_2(\theta)=1+\cos\theta

for

0\le\theta\le\tfrac{\pi}{3}

. What is the exact area of this region? (a)

\dfrac{3\pi}{4}-1

(b)

\dfrac{\pi}{2}

(c)

\pi

(d)

\dfrac{\sqrt{3}}{2}-\dfrac{\pi}{6}