Polar Coordinates

Conversion

Polar to Cartesian

$$x=r\cos (\theta )y=r\sin (\theta )$$

Cartesian to Polar

$$r^2=x^2+y^2$$

Double Integral

$$\iint f(x,y)dA={\int }_{\theta =\alpha }^{\theta =\beta }{\int }_{r=h_1(\theta )}^{r=h_2(\theta )}f(r\cos (\theta ),r\sin (\theta ))rdrd\theta$$