# evaluating multiple integrals: polar coordinates

(1.3 hours to learn)

## Summary

A common trick for computing double integrals is to transform them into a polar coordinate representation. Canonical examples include integrating a Gaussian and computing moments of inertia.

## Context

This concept has the prerequisites:

## Core resources (read/watch one of the following)

## -Free-

→ MIT Open Courseware: Multivariable Caclulus (2010)

Video lectures for MIT's introductory multivariable calculus class.

## -Paid-

→ Multivariable Calculus

An introductory multivariable calculus textbook.

Location:
Section 14.4, "Double integrals in polar coordinates," pages 961-966

→ Multivariable Mathematics

A textbook on linear algebra and multivariable calculus with proofs.

Location:
Section 7.3, "Polar, cylindrical, and spherical coordinates," pages 288-296

## See also

- This trick can be generalized to three dimensions: This trick is an instance of the more general notion of change of variables .