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

See Examples For:

line integral

Because of Equation 6.9, we often use the notation ∫CF · dr for the line integral ∫CF · Tds.

From Textbooks ● Mar. 30, 2016

Before looking at how to compute a line integral, we need to examine the geometry captured by these integrals.

From Textbooks ● Mar. 30, 2016

Figure 6.23 The flux of vector field F across curve C is computed by an integral similar to a vector line integral.

From Textbooks ● Mar. 30, 2016

If we think of the line integral as computing work, then this makes sense: if you hike up a mountain, then the gravitational force of Earth does negative work on you.

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 Andrew Gray