APFIVE Total Area of a Polar Region
Which of the following gives the total area enclosed by the graph of the polar curve $$r = \theta \sin 2\theta$$ for $$0 \leq \theta \leq 2\pi$$?
A
$$\displaystyle \int_{0}^{2\pi} \frac{1}{2} (\theta \sin 2\theta)^2\, d\theta$$
B
$$\displaystyle \int_{0}^{2\pi} |\theta \sin 2\theta|\, d\theta$$
C
$$\displaystyle \int_{0}^{2\pi} (\theta \sin 2\theta)^2\, d\theta$$
D
$$\displaystyle \int_{0}^{2\pi} \frac{1}{2} |\theta \sin 2\theta|\, d\theta$$
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