Mathematics

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}

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

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

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