Two polar curves are given by and

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

Problem

Two polar curves are given by r1(θ)=3 r_1(\theta)=3 and r2(θ)=2sin⁡θ r_2(\theta)=2\sin\theta , with 0≤θ≤π2 0\le\theta\le\tfrac{\pi}{2} . The region of interest is enclosed between the two curves and the rays θ=0 \theta=0 and θ=π2 \theta=\tfrac{\pi}{2} . (a) Write a definite integral whose value equals the exact area of the region contained between the two curves on the stated interval. Do not evaluate yet. (b) Evaluate the integral from part (a) to obtain the exact area. Express your answer in terms of π\pi.

Related theory

Browse the problem library