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

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

We can extend the concept of a line integral to a surface integral to allow us to perform this integration.

From Textbooks • Mar. 30, 2016

Calculate the line integral of G over C1.

From Textbooks • Mar. 30, 2016

In the next example, the double integral is more difficult to calculate than the line integral, so we use Green’s theorem to translate a double integral into a line integral.

From Textbooks • Mar. 30, 2016

If it is made endless, the magnetic force H is the same everywhere along the central axis and the line integral along the axis is Hl.

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