Volume integral

In mathematics—in particular, in 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 mathematics—in particular, in 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. It can also mean a triple integral within a region D ⊂ R 3 {displaystyle Dsubset mathbb {R} ^{3}} of a function f ( x , y , z ) , {displaystyle f(x,y,z),} and is usually written as: A volume integral in cylindrical coordinates is and a volume integral in spherical coordinates (using the ISO convention for angles with φ {displaystyle varphi } as the azimuth and θ {displaystyle heta } measured from the polar axis (see more on conventions)) has the form Integrating the function f ( x , y , z ) = 1 {displaystyle f(x,y,z)=1} over a unit cube yields the following result: