Subsections

# Double integrals with Maple

## Purpose

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

## Getting Started

To assist you, there is a worksheet associated with this lab that contains examples and even solutions to some of the exercises. You can copy that worksheet to your home directory by going to your computer's Start menu and choose run. In the run field type:

\\filer\calclab


when you hit enter, you can then choose MA1024 and then choose the worksheet

Doubleint_start_C13.mw


Remember to immediately save it in your own home directory. Once you've copied and saved the worksheet, read through the background on the internet and the background of the worksheet before starting the exercises.

## Background

### Volumes from double integrals

Suppose that is a rectangular region in the the plane, and that is a continuous, non-negative function on . Then the volume of the solid above and below is given by the double integral

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. It also has an example of how to use Maple if the region of integration is of the more complicated form . This is the case where the base of the solid is not rectangular, but is bounded by two curves and . If is as before, then the volume of the solid above and below is given by

The other case, where the region is -simple can also be handled using Maple, and there is an example in the worksheet.

## Exercises

1. Use Maple to compute the following double integrals.
a)

b)

c)

2. Let be the region in the plane bounded by the two curves and . Use a double integral to compute the area of the region. Use both orders of integration. Include a plot of the region in your worksheet.
3. Use a double integral to find the volume of the region bounded by the two paraboloids and .