# Line integral

From AMS Glossary

## line integral

The integral of a function along a given curve.

Mathematically, if where where

*s*is a linear coordinate along the curve, the line integral of a function*f*(*s*) between points*A*and*B*on the curve is*f*(*s*) is evaluated on the curve. The line integral of a vector field**F**along the same curve is*d***r**is a vector element along the curve of magnitude*ds*. In general the integral will depend on the curve; in the special case where the field**F**is irrotational, it depends only on the points*A*and*B*and therefore vanishes for a closed curve. In meteorology, line integrals are of frequent occurrence, for example, in the circulation, and in the averaging of a quantity along a latitude circle.