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 .