The curve encloses a finite region in the plane

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

Problem

The curve r=4cos⁡θr=4\cos\theta encloses a finite region in the plane. Which of the following definite integrals correctly represents the area of that region? (a) ∫−π/2π/2(4cos⁡θ)2 dθ\displaystyle \int_{-\pi/2}^{\pi/2}(4\cos\theta)^2\,d\theta (b) 12∫0π/2(4cos⁡θ)2 dθ\displaystyle \tfrac12\int_{0}^{\pi/2}(4\cos\theta)^2\,d\theta (c) 12∫−π/2π/2(4cos⁡θ)2 dθ\displaystyle \tfrac12\int_{-\pi/2}^{\pi/2}(4\cos\theta)^2\,d\theta (d) 12∫0π(4cos⁡θ)2 dθ\displaystyle \tfrac12\int_{0}^{\pi}(4\cos\theta)^2\,d\theta

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