For , a region is bounded by the curve and the origin. What is the exact area of…

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

Problem

For

0 \le \theta \le \dfrac{\pi}{3}

, a region

R

is bounded by the curve

r = 6\sin\theta

and the origin. What is the exact area of

R

? (a)

3\pi + \dfrac{9\sqrt{3}}{4}

(b)

3\pi - \dfrac{9\sqrt{3}}{4}

(c)

6\pi - \dfrac{9\sqrt{3}}{2}

(d)

3\pi - \dfrac{9\sqrt{3}}{2}