# evaluating multiple integrals: change of variables

(1.3 hours to learn)

## Summary

A useful trick for computing multiple integrals is to find a simpler parameterization of the region and apply the change of variables formula.

## Context

This concept has the prerequisites:

- determinant and volume
- evaluating multiple integrals: polar coordinates (Polar coordinates are an instructive example.)
- determinant (The change of variables formula involves the determinant of the Jacobian.)
- linear approximation (The change of variables formula involves a linear approximation to the transformation.)

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

## -Free-

→ MIT Open Courseware: Multivariable Caclulus (2010)

Video lectures for MIT's introductory multivariable calculus class.

Location:
Session 53, "Change of variables"

## -Paid-

→ Multivariable Calculus

An introductory multivariable calculus textbook.

Location:
Section 14.9, "Change of variables in multiple integrals," pages 1001-1007

→ Multivariable Mathematics

A textbook on linear algebra and multivariable calculus with proofs.

Location:
Section 7.6, "Change of Variables Theorem," pages 324-331

Other notes:

- You can skip the proofs as far as this node is concerned.

## See also

- Some particular examples of this trick: We use the same change of variables formula to determine the PDF of a function of a continuous random variable .