Surface integral

It has been suggested that Volume element#Area element of a surface be merged into this article. (Discuss) Proposed since December 2023.

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Calculus
${\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}$
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In mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral. Given a surface, one may integrate over this surface a scalar field (that is, a function of position which returns a scalar as a value), or a vector field (that is, a function which returns a vector as value). If a region R is not flat, then it is called a surface as shown in the illustration.

Surface integrals have applications in physics, particularly with the theories of classical electromagnetism.