Let be the region that lies inside the cardioid and outside the circle

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

Problem

Let

R

be the region that lies inside the cardioid

r = 2\bigl(1+\cos\theta\bigr)

and outside the circle

r = 2

. What is the exact area of

R

? (a)

3\pi + 8

(b)

\pi

(c)

\pi + 8

(d)

2\pi