MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions
Problem
Consider the polar curves C1:r=2+sinθ and C2:r=2 for 0≤θ≤2π.
(a) Determine all values of θ in [0,2π] for which the two curves intersect.
(b) Explain why any additional solutions of the equation obtained in part (a) that fall outside the interval [0,2π] do not correspond to new points of intersection in the plane.
(c) Write, but do not evaluate, a definite integral that gives the exact area of the region that lies inside C1 and outside C2 between the two smallest positive intersection angles.
(d) Describe how the limits of integration and the integrand in part (c) would change if the region of interest were instead the portion lying inside C2 and outside C1 on the interval between the two largest intersection angles.