Mathematics

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

\dfrac{\pi}{2}

\pi

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