### Introduction

A vector or scalar field - including one formed from a vector derivative (div, grad or curl) - can be integrated over a surface or volume. This Section shows how to carry out such operations.

#### Prerequisites

- be familiar with vector derivatives
- be familiar with double and triple integrals

#### Learning Outcomes

- carry out operations involving integrations of scalar and vector fields

#### Contents

1 Surface integrals involving vectors1.1 The unit normal

1.2 $\underset{\u0332}{dS}$ and the unit normal

1.3 Integrating a scalar field

1.4 Integrating a vector field

2 Engineering Example 4

2.1 Magnetic flux

3 Engineering Example 5

3.1 The current continuity equation

4 Volume integrals involving vectors