Study guide and 2 practice problems on:

## Double integrals in polar coordinates

Consider a double integral $\iint_Df(x,y) dA$.
In polar coordinates, the differential area element $dA = r dr d\theta$.
Hence, $\iint_D f(x,y) dA = \iint_\tilde{D} f(r,\theta) r dr d\theta$, where $\tilde{D}$ is the region $D$ expressed in polar coordinates.
If $f(x,y)$ involves terms like $x^2 + y^2$ and $D$ is easy to describe using $r$ and $\theta$, it may be convenient to change to polar coordinates.