For , the curves and bound a region. What is the exact area of this…

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

Problem

For

0\le\theta\le\pi

, the curves

r=\sin\theta

and

r=\sin 2\theta

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

\dfrac{3\sqrt3}{32}

(b)

\dfrac{3\sqrt3}{16}

(c)

\dfrac{\sqrt3}{16}

(d)

\dfrac{3\sqrt3}{8}