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

Informally, the surface integral of a scalar-valued function is an analog of a scalar line integral in one higher dimension.

From Textbooks • Mar. 30, 2016

As long as we have a potential function, calculating the line integral is only a matter of evaluating the potential function at the endpoints and subtracting.

From Textbooks • Mar. 30, 2016

By Green’s theorem, the flux across each approximating square is a line integral over its boundary.

From Textbooks • Mar. 30, 2016

Therefore, the definition of a surface integral follows the definition of a line integral quite closely.

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