# Plane Areas in Polar Coordinates | Applications of Integration

The fundamental equation for finding the area enclosed by a curve whose equation is in polar coordinates is...

$\displaystyle A = \frac{1}{2}{\int_{\theta_1}^{\theta_2}} r^2 \, d\theta$

Where θ_{1} and θ_{2} are the angles made by the bounding radii.

The formula above is based on a sector of a circle with radius *r* and central angle *d*θ. Note that *r* is a polar function or *r* = *f*(θ). See figure above.