### Introduction

In the previous Section we saw how to evaluate double integrals over simple rectangular regions. We now see how to extend this to non-rectangular regions.

In this Section we introduce functions as the limits of integration, these functions define the region over which the integration is performed. These regions can be non-rectangular. Extra care now must be taken when changing the order of integration. Producing a sketch of the region is often very helpful.

#### Prerequisites

• have a thorough understanding of the various techniques of integration
• be familiar with the concept of a function of two variables
• have completed Section 27.1
• be able to sketch a function in the plane

#### Learning Outcomes

• evaluate double integrals over non-rectangular regions