### Introduction

One of the important applications of integration is to find the area bounded by a curve. Often such an area can have a physical significance like the work done by a motor, or the distance travelled by a vehicle. In this Section we explain how such an area is calculated.

#### Prerequisites

- understand integration as the reverse of differentiation
- be able to use a table of integrals
- be able to evaluate definite integrals
- be able to sketch graphs of common functions including polynomials, simple rational functions, exponential functions and trigonometric functions

#### Learning Outcomes

- find the area bounded by a curve and the $x$ -axis
- find the area between two curves

#### Contents

1 Calculating the area under a curve2 The area bounded by a curve lying above the x-axis

3 The area bounded by a curve, not entirely above the x-axis