Mathematics

Mathematics

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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