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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 /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.
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.
 a)

 b)

 c)

 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.
 Use a double integral to find the volume of the region bounded by the two paraboloids and .
 Use a double integral to prove that the volume of a sphere of radius is
.
Next: About this document ...
Up: lab_template
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Dina Solitro
20060411