A region is formed by two parts: • Part I: the sector bounded by the circle for

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

Problem

A region is formed by two parts: • Part I: the sector bounded by the circle

r = 2

for

0 \le \theta \le \dfrac{\pi}{6}

. • Part II: the region bounded by the curve

r = 4\sin\theta

for

\dfrac{\pi}{6} \le \theta \le \dfrac{\pi}{2}

. Determine the exact total area of the region. (a)

\dfrac{4\pi}{3}+\sqrt{3}

(b)

\dfrac{5\pi}{3}

(c)

\dfrac{5\pi}{3}+\sqrt{3}

(d)

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