### Introduction

especially true when modelling waves and alternating current circuits. When the root-mean-square (rms) value of a waveform, or signal is to be calculated, you will often find this results in an integral of the form

$\phantom{\rule{2em}{0ex}}\int {sin}^{2}t\phantom{\rule{0.3em}{0ex}}dt$

In this Section you will learn how such integrals can be evaluated.

#### Prerequisites

- be able to find a number of simple definite and indefinite integrals
- be able to use a table of integrals
- be familiar with standard trigonometric identities

#### Learning Outcomes

- use trigonometric identities to write integrands in alternative forms to enable them to be integrated

#### Contents

1 Integration of trigonometric functions2 Engineering Example 3

2.1 Magnetic flux

3 Orthogonality relations

4 Reduction formulae

5 Harder trigonometric integrals