Total Area of a Polar Region

Question

Which of the following represents the total area enclosed by the polar curve $$r = 	heta \sin 2	heta$$ for $$0 \leq 	heta \leq 2\pi$$?

Accepted Answer

$$\displaystyle \int_{0}^{2\pi} \frac{1}{2} (	heta \sin 2	heta)^2\, d	heta$$

Answer

$$\displaystyle \int_{0}^{2\pi} (	heta \sin 2	heta)^2\, d	heta$$

Answer

$$\displaystyle \int_{0}^{2\pi} |	heta \sin 2	heta|\, d	heta$$

Answer

$$\displaystyle \int_{0}^{2\pi} \frac{1}{2} |	heta \sin 2	heta|\, d	heta$$

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