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

where the ${\displaystyle u_{i}}$ are the coordinates, so that the volume of any set ${\displaystyle B}$ can be computed by

For example, in spherical coordinates ${\displaystyle dV=u_{1}^{2}\sin u_{2}\,du_{1}\,du_{2}\,du_{3}}$, and so ${\displaystyle \rho =u_{1}^{2}\sin u_{2}}$.

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