Area Between Two Polar Curves

Area Between Two Polar Curves

If the outer and inner curves are:

$$r=r_1(\theta),\quad r=r_2(\theta)$$

then the area between them is:

$$A=\frac{1}{2}\int_\alpha^\beta\left(r_1^2-r_2^2\right)d\theta$$

Usage

- Used when one polar curve lies completely outside another over the interval.