The three-petaled rose curve intersects itself at the pole
MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions
Problem
The three-petaled rose curve r=5sin(3θ) intersects itself at the pole. A sector region S is bounded by the portion of the curve traced from θ=0 to θ=32π and by the initial ray θ=0.
(1) Write a sum of one or more definite integrals whose combined value equals the exact area of S. Be sure each integral has correct limits so that no portion of the curve is counted more than once.
(2) Evaluate the integrals obtained in part (a) to find the exact area of region S.