The circle completely contains the lemniscate

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

The circle r=3r = 3 completely contains the lemniscate r=3cos⁡2θr = 3 \cos 2\theta . Which of the following integrals gives the exact area of the lemniscate? (a) 2∫0π/412(3cos⁡2θ)2 dθ\displaystyle 2\int_{0}^{\pi/4} \tfrac12\bigl(3\cos 2\theta\bigr)^2\,d\theta (b) 4∫0π/412(3cos⁡2θ)2 dθ\displaystyle 4\int_{0}^{\pi/4} \tfrac12\bigl(3\cos 2\theta\bigr)^2\,d\theta (c) 4∫0π/212(3cos⁡2θ)2 dθ\displaystyle 4\int_{0}^{\pi/2} \tfrac12\bigl(3\cos 2\theta\bigr)^2\,d\theta (d) 4∫0π/4(3cos⁡2θ)2 dθ\displaystyle 4\int_{0}^{\pi/4} \bigl(3\cos 2\theta\bigr)^2\,d\theta

Related theory

Browse the problem library