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

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

From Textbooks • Mar. 30, 2016

Calculate the line integral of G over C1.

From Textbooks • Mar. 30, 2016

Figure 6.79 Stokes’ theorem relates the flux integral over the surface to a line integral around the boundary of the surface.

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

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