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

Example Sentences

See Examples For:

line integral

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

If we think of the line integral as computing work, then this makes sense: if you hike up a mountain, then the gravitational force of Earth does negative work on you.

From Textbooks ● Mar. 30, 2016

As long as we have a potential function, calculating a line integral using the Fundamental Theorem for Line Integrals is much easier than calculating without the theorem.

From Textbooks ● Mar. 30, 2016

The result is the scalar line integral of the function over the curve.

From Textbooks ● Mar. 30, 2016

If, for instance, we carry a unit pole in a circular path of radius r once round an infinitely long straight filamentary current I, the line integral is 4πI.

From Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 2 "Ehud" to "Electroscope" by Various