Volume integral

A volume integral or triple integral is in mathematics, a special case of the multidimensional integral calculus, which finds application in physics in particular. Is an integral, in which a function is integrated three times consecutively, each with a direction of a three-dimensional space. This must be a volume of a geometric body but not necessarily. There are various forms, generally presenting this bill:

For ease of illustration, only a single integral sign is often written and only announced the integration volume by a large V:

Application

Volume integrals are used in many physical problems. So can be calculated from all densities with a volume integration of the relevant underlying variables, such as the electric charge from the charge density or the mass of the (mass) density. Also, the Gaussian integral theorem, which in electrodynamics is particularly important based on a volume integral. The probability density of the velocity magnitude in the Maxwell -Boltzmann distribution is obtained by volume integration over the distribution of the individual directions of the velocity vector - this is an example of a volume integral of a non- geometric volume.

Postgraduate

• IN Bronstein, KA Semendjajew: Handbook of Mathematics. 6th edition. Verlag Harri German, Frankfurt am Main 2006, ISBN ISBN 978-3-8171-2006-2.

• Integral calculus