Let be the region that lies inside both of the curves and

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

Problem

Let

R

be the region that lies inside both of the curves

r=2\sin\theta

and

r=1

. What is the exact area of

R

? (a)

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

(b)

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

(c)

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

(d)

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