Polar Surface Area About the Polar Axis

Polar Surface Area About the Polar Axis

For a polar curve:

$$r=f(\theta)$$

the surface area generated about the polar axis is:

$$S=2\pi\int_\alpha^\beta r\sin\theta\sqrt{r^2+\left(\frac{dr}{d\theta}\right)^2}\,d\theta$$

Usage

- Used for advanced surface-of-revolution problems involving polar curves.