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

This same kind of geometric argument can be extended to show that the line integral of a three-variable function over a curve in space does not depend on the parameterization of the curve.

From Textbooks ● Mar. 30, 2016

You may have noticed a difference between this definition of a scalar line integral and a single-variable integral.

From Textbooks ● Mar. 30, 2016

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

Figure 6.23 The flux of vector field F across curve C is computed by an integral similar to a vector line integral.

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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