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

Calculate the line integral of F over C1.

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

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

From Textbooks • Mar. 30, 2016

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

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