# Surface integral

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 a scalar field (that is, a function of position which returns a scalar as a value) over the surface, 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.

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