Volume integral
In mathematics (particularly multivariable calculus), a volume integral (∭) refers to 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. In coordinates. It can also mean a triple integral within a region formula_1 of a function formula_2 and is usually written as: formula_3 A volume integral in cylindrical coordinates is formula_4 and a volume integral in spherical coordinates (using the ISO convention for angles with formula_5 as the azimuth and formula_6 measured from the  polar axis (see more on conventions)) has the form formula_7 Example. Integrating the equation formula_8 over a unit cube yields the following result: formula_9 So the volume of the unit cube is 1 as expected. This is rather trivial however, and a volume integral is far more powerful. For instance if we have a scalar density function on the unit cube then the volume integral will give the total mass of the cube. For example for density function: formula_10 the total mass of the cube is: formula_11