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Subsections
The purpose of this lab is to acquaint you with using Maple to do
double integrals.
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.
Suppose that is a rectangular region in the the plane, and
that is a continuous, nonnegative 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.
 Use Maple to compute the following double integrals.




 Let be the region in the plane containing the origin and
bounded by the two curves
and . Compute
where
. Include a plot of the region in your
worksheet.
 Consider the following integral
where the region is bounded by , , and
. First, plot the region . Then
compute the integral using as the inner variable of integration.
Repeat the calculuation using as the inner variable of
integration. You should get the same answer.
 Use a double integral to find the volume of the region beneath
the plane with equation and above the triangle with
vertices , , and . Include a plot of the region
in the plane.
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William W. Farr
20020920