Section 4
Multiple Integrals
By Boundless
![Thumbnail](../../../../../../figures.boundless-cdn.com/17897/square/volume-under-surface.jpg)
For a rectangular region
![Thumbnail](../../../../../../figures.boundless-cdn.com/17896/square/volume-under-surface.jpg)
An iterated integral is the result of applying integrals to a function of more than one variable.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17903/raw/mpio-formulediriduzione-r2.jpg)
Double integrals can be evaluated over the integral domain of any general shape.
![Thumbnail](../../../../../../figures.boundless-cdn.com/18220/raw/minio-da-cartesiano-polare.jpg)
When domain has a cylindrical symmetry and the function has several specific characteristics, apply the transformation to polar coordinates.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17905/raw/cylindrical-coordinates.jpg)
When the function to be integrated has a cylindrical symmetry, it is sensible to integrate using cylindrical coordinates.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17906/raw/colatitude-2c-longitude-29.jpg)
When the function to be integrated has a spherical symmetry, change the variables into spherical coordinates and then perform integration.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17908/raw/-normalit-c3-a0-r3-esempio.jpg)
For
![Thumbnail](../../../../../../figures.boundless-cdn.com/18271/raw/cylindrical-coordinates.jpg)
One makes a change of variables to rewrite the integral in a more "comfortable" region, which can be described in simpler formulae.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17909/raw/stribution-xy-line-segment.jpg)
Multiple integrals are used in many applications in physics and engineering.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17910/square/orbit3.gif)
The center of mass for a rigid body can be expressed as a triple integral.