# Volume integral

In mathematics—in particular, in multivariable calculus—a volume integral refers to an integral over a 3-dimensional domain.

It can also mean a triple integral within a region D in R3 of a function $f(x,y,z),$ and is usually written as:

$\iiint\limits_D f(x,y,z)\,dx\,dy\,dz.$

A volume integral in cylindrical coordinates is

$\iiint\limits_D f(r,\theta,z)\,r\,dr\,d\theta\,dz,$

and a volume integral in spherical coordinates (using the convention for angles with $\theta$ as the azimuth and $\phi$ measured from the polar axis (see more on conventions)) has the form

$\iiint\limits_D f(\rho,\theta,\phi)\,\rho^2 \sin\phi \,d\rho \,d\theta\, d\phi .$