APFIVE Which of the following correctly contrasts the formula for the area of the region bounded by the polar curve $$r=f(\theta)$$ from $$\theta=a$$ to $$\theta=b$$ with the formula for the area of a circular sector?
The area enclosed by a polar curve uses $$\frac{1}{2}\int_{a}^{b} [f(\theta)]^2 d\theta$$, while the area of a sector uses $$\frac{1}{2}r^2(\theta_2 - \theta_1)$$.
The area enclosed by a polar curve uses $$\frac{1}{2}\int_{a}^{b} [f(\theta)]^2 d\theta$$, while the area of a sector uses $$r(\theta_2 - \theta_1)$$.
The area enclosed by a polar curve uses $$\pi\int_{a}^{b} [f(\theta)]^2 d\theta$$, while the area of a sector uses $$\frac{1}{2}r^2(\theta_2 - \theta_1)$$.
The area enclosed by a polar curve uses $$\int_{a}^{b} f(\theta) d\theta$$, while the area of a sector uses $$\frac{1}{2}r^2(\theta_2 - \theta_1)$$.
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