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

Changing the parameterization did not change the value of the line integral.

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

The result is the scalar line integral of the function over 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

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