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
or
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.
> int(int(x^2+y^2,x=-2..1),y=0..1);
> int(int(x^2+y^2,y=0..1),x=-2..1);
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
> int(int(x^2+y^2,y=-sqrt(1-(x-1)^2)..sqrt(1-(x-1)^2)),x=0..2);
