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

Since ∫ F • dr ≠ ∫ F • dr, the value of a line integral of F depends on the path between two given points.

From Textbooks • Mar. 30, 2016

The definition of a scalar line integral can be extended to parameter domains that are not rectangles by using the same logic used earlier.

From Textbooks • Mar. 30, 2016

In the preceding two examples, the double integral in Green’s theorem was easier to calculate than the line integral, so we used the theorem to calculate the line integral.

From Textbooks • Mar. 30, 2016

We have seen that a line integral is an integral over a path in a plane or in space.

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