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.

---

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

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

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

From Textbooks • Mar. 30, 2016

Again, notice the similarities between this definition and the definition of a scalar line integral.

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