APFIVE How does the formula for calculating the area enclosed by a polar curve $$r=f(\theta)$$ from $$\theta=a$$ to $$\theta=b$$ differ from the formula for the area of a sector in polar coordinates?
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 $$\frac{1}{2}\int_{a}^{b} [f(\theta)]^2 d\theta$$, 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 $$\int_{a}^{b} f(\theta) d\theta$$, while the area of a sector uses $$\frac{1}{2}r^2(\theta_2 - \theta_1)$$.
Question Leaderboard
| Rank | |||||
|---|---|---|---|---|---|
| #1 | pietroamola | 2 | 2 | 0m 00s | 200 |
| #2 | lluatic | 0 | 1 | 0m 39s | -49 |
| #3 | yeee5864 | 1 | 3 | 4h 49m | -17,282 |