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In mathematics, a surface integral is a definite integral taken over a surface (which may be a curve set in space). Just as a line integral allows one to integrate over an arbitrary curve (of one dimension), a surface integral can be thought of as a double integral integrating over a two-dimensional surface. Given a surface, one may integrate over its scalar fields (that is, functions which return numbers as values), or its vector fields (that is, functions which return vectors as values).
Surface integrals have applications in physics, particularly with the classical theory of electromagnetism.