Study guide and 2 practice problems on:

Double integrals in polar coordinates

$\newcommand{\bfA}{\mathbf{A}}$ $\newcommand{\bfB}{\mathbf{B}}$ $\newcommand{\bfC}{\mathbf{C}}$ $\newcommand{\bfF}{\mathbf{F}}$ $\newcommand{\bfI}{\mathbf{I}}$ $\newcommand{\bfa}{\mathbf{a}}$ $\newcommand{\bfb}{\mathbf{b}}$ $\newcommand{\bfc}{\mathbf{c}}$ $\newcommand{\bfd}{\mathbf{d}}$ $\newcommand{\bfe}{\mathbf{e}}$ $\newcommand{\bfi}{\mathbf{i}}$ $\newcommand{\bfj}{\mathbf{j}}$ $\newcommand{\bfk}{\mathbf{k}}$ $\newcommand{\bfn}{\mathbf{n}}$ $\newcommand{\bfr}{\mathbf{r}}$ $\newcommand{\bfu}{\mathbf{u}}$ $\newcommand{\bfv}{\mathbf{v}}$ $\newcommand{\bfw}{\mathbf{w}}$ $\newcommand{\bfx}{\mathbf{x}}$ $\newcommand{\bfy}{\mathbf{y}}$ $\newcommand{\bfz}{\mathbf{z}}$
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.

Related topics

Practice problems