MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions
Problem
Consider the polar curves r1=4cosθ and r2=2. The bounded region of interest is enclosed by portions of both curves.
(a) Solve for all values of θ in [0,2π] at which the two curves intersect.
(b) Using the results of part (a), determine the precise θ-intervals that trace exactly the finite region enclosed by the two curves (no overlap, no gaps).
(c) Write an exact integral expression (or sum of integrals) whose value equals the area of this region.
(d) Evaluate the integral(s) obtained in part (c) to obtain the exact area.