MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions
Problem
Consider the polar curves r=1 and r=2sinθ on the interval 0≤θ≤π. Let D be the region bounded between the two curves.
(1) Part 1: (a) Without performing any calculations, provide a qualitative sketch of both curves on the given interval and indicate the region D.
(2) Part 2: (b) Identify all values of θ in 0≤θ≤π where the two curves intersect, and explain how you determined those values.
(3) Part 3: (c) Describe, in complete sentences, how you would set up the definite integral(s) required to compute the exact area of D. Your description should include appropriate limits of integration and which curve serves as the outer and inner radius on each sub-interval, but you do NOT need to evaluate the integral(s).