# Chapter 23: Reducing a Line Integral to an Ordinary Integral and Related Reductions

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## Introduction

Though a line integral on a path P is most easily evaluated when the integrand
can be expressed as a gradient and the integral becomes a difference between
values of a function at the endpoints of P, we here consider the process for
reducing line integrals to ordinary ones. We also describe how to make a Surface
flux integral into a two dimensional integral over an area in the plane.

## Topics

23.1 Making a Line Integral into an Ordinary
Integral

23.2 Examples

23.3 Practical Comments

23.4 Multiple Integrals and Area Integrals