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. 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 /math/calclab/MA1024/Doubleint_start.mws ~/My_Documents


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

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)

d)

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. Include a plot of the region in your worksheet.

3. Let be the region in the plane bounded by the curves and . Find the area of the region using both orders of integration. Include a plot of the region in your worksheet.