# Chapter 31: Doing Area, Surface and Volume Integrals

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## Introduction

Most of your encounters with these integrals will not require you to evaluate
them. However it is a good idea to develop some experience in doing so, to build
your confidence in them. One of these is generally done by your performing a
multiple integration, which means a sequence of ordinary integrations. To do
so you must do three things: determine the integrand as a function of your variables
of integration; determine the area or volume element of the integral in terms
of same; and find appropriate limits of integration on the ordinary integrals
obtained. Once this is done you then perform ordinary integrations. We discuss
these steps here.

## Topics

31.1 Introduction

31.2 Expressing Surfaces Parametrically
or in Appropriate Form for Integrations

31.3 Determining the Integrand

31.4 Determining the Area or Volume Element

31.5 Setting up Correct Limits of Integration

31.6 Doing the Integrals