An integral over a volume, which can involve vectors and scalars. The volume element dV=dxdydz is a scalar. For a vector function F(x,y,z) the volume integral is given by ʃvFdV. For a scalar function ϕ(x,y,z) the volume integral is given by ʃvϕdV.
Electronics and Electrical Engineering
An integral over a volume element of some function of 3D space. For example, if the function gives the density of material at points in space, then a volume integral of that function over some region of that space will yield as a result the mass of that region. In Cartesian coordinates a triple integral is used; this means that if the density function is ρ and the region is D, then the mass is given by: