---
tag: 02QJVFCNYD
kind: concept
name: Line integral of a scalar field
aliases: [scalar-line-integral, integral-with-respect-to-arc-length]
msc: [26B12]
uses: [0G7WM8DX4P, 0HATW2VWAZ, 0JPCHTXWG0]
sources:
  - url: https://en.wikipedia.org/wiki/Line_integral
    locator: Line integral of a scalar field
---

## Summary

The line integral of a scalar field along a curve adds up the values of the field along the curve. Each value is weighted by a small length of the curve.
For a non-negative field on a plane curve, it is the area of the curtain between the curve and the graph of the field.