line integral

American  

noun

Mathematics.

1. 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.

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Etymology

Origin of line integral

First recorded in 1870–75

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Example Sentences

See Examples For:

line integral

The line integral of vector field F along an oriented closed curve is called the circulation of F along C. Circulation line integrals have their own notation: ∮CF · Tds.

From Textbooks ● Mar. 30, 2016

Note that in a scalar line integral, the integration is done with respect to arc length s, which can make a scalar line integral difficult to calculate.

From Textbooks ● Mar. 30, 2016

The result is the scalar line integral of f along C.

From Textbooks ● Mar. 30, 2016

Therefore, the line integral in Example 6.21 can be written as ∫C−2ydx + 2xdy.

From Textbooks ● Mar. 30, 2016

It is now well known as Stokes's theorem connecting a certain surface integral with a line integral, and has many applications both in physics and in geometry.

From Lord Kelvin An account of his scientific life and work by Andrew Gray

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