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). 