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.

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.

- 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.
- 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. - Use a double integral to find the volume of the region bounded by the two paraboloids and .

2008-04-16