Subsections

# MA 1024 Lab 5: Double integrals

## Purpose

The purpose of this lab is to acquaint you with using Maple to evaluate double integrals.

## Getting Started

To assist you, there is a worksheet associated with this lab that contains examples. You can copy that worksheet to your home directory with the following command, which must be run in a terminal window, not in Maple.

cp ~bfarr/DoubleInt_start.mws ~


You can copy the worksheet now, but you should read through the lab before you load it into Maple. Once you have read to the exercises, start up Maple, load the worksheet DoubleInt_start.mws, and go through it carefully. Then you can start working on the exercises.

## Background

### Computing double integrals

Suppose that is a rectangular region in the the plane, and that is a continuous function on . Then the double integral of over is denoted by

You learned in class that such integrals can be evaluated by either of the iterated integrals

or

where the rectangle is defined by the inequalities and . The worksheet associated with this lab contains examples of how to use Maple to compute double integrals over rectangular regions.

It is also possible to use Maple to compute double integrals over regions that are not rectangles. The only hard part is setting up the limits of integration. The worksheet contains examples of how to use Maple to help you do this.

## Exercises

1. Use Maple to compute the following double integrals.

2. Consider the following integral

where the region is bounded by , , and . Compute the integral using as the inner variable of integration and then repeat the calculuation using as the inner variable of integration. You should get the same answer.