Let and . These curves enclose a finite region that lies entirely in the first…

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

Problem

Let

r_1(\theta)=2\sin\theta

and

r_2(\theta)=\sin\theta+1

. These curves enclose a finite region that lies entirely in the first quadrant. What is the exact area of this region? (a)

\dfrac{\pi}{8}-1

(b)

2-\dfrac{\pi}{4}

(c)

1-\dfrac{\pi}{8}

(d)

\dfrac{3\pi}{8}-1