Which of the following integrals correctly represents the area enclosed by the polar…

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

Problem

Which of the following integrals correctly represents the area enclosed by the polar curve r=3sin⁡θr = 3\sin\theta for 0≤θ≤π0 \le \theta \le \pi? (a) ∫0π(3sin⁡θ)2 dθ\displaystyle \int_{0}^{\pi} (3\sin\theta)^2\, d\theta (b) 12∫0π3sin⁡θ dθ\displaystyle \tfrac12 \int_{0}^{\pi} 3\sin\theta\, d\theta (c) 12∫0π(3sin⁡θ)2 dθ\displaystyle \tfrac12 \int_{0}^{\pi} (3\sin\theta)^2\, d\theta (d) 12∫0π/2(3sin⁡θ)2 dθ\displaystyle \tfrac12 \int_{0}^{\pi/2} (3\sin\theta)^2\, d\theta

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