# line integral

- 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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## Origin of line integral^{}

First recorded in 1870–75

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

## Examples from the Web for line integral

### Historical Examples

#### (i.) Any simple integral can be regarded as a line-integral taken along a portion of the axis of x.