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

Such a task requires a new kind of integral, called a line integral.

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

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

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

It is now well known as Stokes's theorem connecting a certain surface integral with a line integral, and has many applications both in physics and in geometry.

From Lord Kelvin An account of his scientific life and work by Gray, Andrew