The circle and the curve enclose a shaded region for

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

Problem

The circle

r=1

and the curve

r=2\sin\theta

enclose a shaded region for

0\le\theta\le\pi

. Find the exact area of this region. (a)

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

(b)

\dfrac{\pi}{6}+\sqrt{3}

(c)

\dfrac{\pi}{3}+\sqrt{3}

(d)

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