A cardioid is given by

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

Problem

r=2+2\sin\theta

. A circle centered at the pole has equation

x^{2}+y^{2}=4

. Compute the area that is inside the cardioid and outside the circle. (a)

16+2\pi

(b)

8+\pi

(c)

2\pi

(d)

8+\dfrac{\pi}{2}