If then
To compute the iterated integral, first find for which so that
Then find for which
and
we find
Putting these together, we have
Let
.
Compute
Let
.
Compute
If the region is defined by a constant bound on with the bound on varying as a function of , then one may compute a double integral over as an iterated integral where one first integrates with respect to and then with respect to .
Let
.
Compute
If the region is a rectangle with horizontal and vertical sides relative to the coordinate axes, the one may compute a double integral over as an iterated integral by first integrating with respect to and then with respect to or vice versa.
Let
.
Compute