We integrate over regions in cylindrical coordinates.

*cylindrical*coordinates.

An ordered triple consisting of a radius, an angle, and a height can be graphed as
meaning:
Coordinates of this type are called

**cylindrical coordinates**.### Triple integrals in cylindrical coordinates

If you want to evaluate this integral you have to change to a region defined in -coordinates, and change to some combination of leaving you with some iterated integral: Now consider representing a region in cylindrical coordinates and let’s express in terms of , , and . To do this, consider the diagram below:

Recalling that the determinate of a matrix gives the volume of a parallelepiped, we could
also deduce the correct form for by setting
and computing:

Write down a triple integral in cylindrical coordinates that will compute the volume
of a cylinder of radius and height .