Surface integral
![The definition of surface integral relies on splitting the surface into small surface elements.](/Images/godic/202501/13/Surface_integral_illustration.svg4034.png")
![An illustration of a single surface element. These elements are made infinitesimally small, by the limiting process, so as to approximate the surface.](/Images/godic/202501/13/Surface_integral1.svg4034.png")
![A vector field on a surface](/Images/godic/202501/13/Surface_vectors4034.png")
In mathematics, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analog of the line integral. Given a surface, one may integrate over its scalar fields (that is, functions which return scalars as values), and vector fields (that is, functions which return vectors as values).