Polar Surface Area About the Initial Line

Polar Surface Area About the Initial Line

For a polar curve:

$$r=f(\theta)$$

the surface area generated about the initial line is:

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

Usage

- Used when the axis of revolution is the initial line in polar coordinates.