Suppose that D is a rectangular region in the the x-y plane, and that is a continuous, non-negative function on D. Then the volume of the solid above D and below is given by the double integral
We learned in class that such integrals can be evaluated by either of the iterated integrals
where the rectangle D is defined by the inequalities and .
Using Maple to evaluate double integrals proceeds in exactly the same fashion. For example, the following Maple commands show the computation of
for both orders of integration.
More complicated integrals are handled similarly. Suppose that we have and we want to know the volume of the solid between the region in the xy plane bounded by the circle and the graph of . Then an appropriate integral is
Using Maple, we calculate this as