In mathematics (particularly multivariable calculus), a volume integral (∭) is an integral over a 3-dimensional domain; that is, it is a special case of multiple integrals. Volume integrals are especially important in physics for many applications, for example, to calculate flux densities, or to calculate mass from a corresponding density function.

In coordinates

It can also mean a triple integral of a function A volume integral in cylindrical coordinates and a volume integral in spherical coordinates measured from the polar axis (see more on conventions The triple integral can be transformed from Cartesian coordinates to any arbitrary coordinate system using the Jacobian matrix and determinant

Example

See also

• Divergence theorem

• Surface integral

• Volume element

• Line element

• Line integral

External links