Let be the cardioid and let be the circle

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

Problem

Let

C_1

be the cardioid

r=1+\cos\theta

and let

C_2

be the circle

r=1

. Write a definite integral (or sum of integrals, if necessary) that represents the exact area of the region that lies inside

C_1

and outside

C_2

. Do not evaluate the integral(s).