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# line integral

the limit, as the norm of the partition of a given curve approaches zero, of the sum of the product of the length of the arcs in the partition times the value of the function at some point on each arc.
[1870-75]

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In mathematics, the integral of a function of several variables defined on a line or curve that has been expressed in terms of arc length (see length of a curve).

An ordinary definite integral is defined over a line segment, whereas a line integral may use a more general path, such as a parabola or a circle. Line integrals are used extensively in the theory of functions of a complex variable.

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also called  Contour Integral,

in mathematics, integral of a function of several variables, defined on a line or curve C with respect to arc length s:

as the maximum segment Δis of C approaches 0. The line integrals

are defined analogously. Line integrals are used extensively in the theory of functions of a complex variable.

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Universalium. 2010.

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