Let and be two polar curves that intersect at and

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

Problem

Let

r = 4\sin\theta

and

r = 2

be two polar curves that intersect at

\theta = \dfrac{\pi}{6}

and

\theta = \dfrac{5\pi}{6}

. Calculate the exact area of the region bounded by the two curves for

0\le \theta \le \pi