# surface integral

surface integral
the limit, as the norm of the partition of a given surface into sections of area approaches zero, of the sum of the product of the areas times the value of a given function of three variables at some point on each section.
[1870-75]

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In calculus, the integral of a function of several variables calculated over a surface.

For functions of a single variable, definite integrals are calculated over intervals on the x-axis and result in areas. For functions of two variables, the simplest double integrals are calculated over rectangular regions and result in volumes. More generally, an integral calculated over a plane or curved surface results in a surface integral representing a volume, though it also has many nongeometric applications.

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Universalium. 2010.

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