### Introduction

When a function
$f\left(x\right)$
is known we can differentiate it to obtain its derivative
$\frac{df}{dx}$
. The reverse process is to obtain the function
$f\left(x\right)$
from knowledge of its derivative. This process is called
**
integration
**
. Applications of integration are numerous and some of these will be explored in subsequent Sections. First, what is important is to practise basic techniques and learn a variety of methods for integrating functions.

#### Prerequisites

- thoroughly understand the various techniques of differentiation

#### Learning Outcomes

- evaluate simple integrals by reversing the process of differentiation
- use a table of integrals
- explain the need for a constant of integration when finding indefinite integrals
- use the rules for finding integrals of sums of functions and constant multiples of functions

#### Contents

1 Integration as differentiation in reverse2 A table of integrals

3 Some rules of integration

3.1 The integral of $k\phantom{\rule{0.3em}{0ex}}f$ ( $x$ ) where $k$ is a constant

3.2 The integral of $f\left(x\right)+g\left(x\right)$ and of $f\left(x\right)-g\left(x\right)$

4 Engineering Example 1

4.1 Electrostatic charge