Volume element
In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates. Thus a volume element is an expression of the form d V = ρ ( u 1 , u 2 , u 3 ) d u 1 d u 2 d u 3 {\displaystyle \mathrm {d} V=\rho (u_{1},u_{2},u_{3})\,\mathrm {d} u_{1}\,\mathrm {d} u_{2}\,\mathrm {d} u_{3}} where the u i {\displaystyle u_{i}} are the coordinates, so that the volume of any set B {\displaystyle B} can be computed by Volume ( B ) = ∫ B ρ ( u 1 , u 2 , u 3 ) d u 1 d u 2 d u 3 .