Let be the rose curve and let be the circle

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

Problem

Let C1C_1 be the rose curve r=5sin⁡(4θ)r=5\sin(4\theta) and let C2C_2 be the circle r=2r=2. A region RR is defined as the set of points that are inside C1C_1 and outside C2C_2. (a) Find all values of θ\theta in [0,2π)[0,2\pi) where the two curves intersect. List them in increasing order. (b) Using your results from part (a), write a sum of definite integrals that represents the exact area of region RR. Do not evaluate the integrals in this part. (c) Evaluate the integrals from part (b) to obtain the exact area of region RR. Express your final answer in terms of π\pi.

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