Polar Area and Sector Area Formulas

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 $\int_{a}^{b} f(\theta) d\theta$, 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 $\frac{1}{2}r^2(\theta_2 - \theta_1)$.