One useful way to think about the evaluation of double integrals is to consider a series of slabs. For y-constant slabs, the height of any slab at some point(x, y0), where y0 is the constant value of y for that particular slab, is given as f(x, y0), so the area of the non-rectangular side of the slab is

∫x(min)x(max)f(x, y0)dx.

The slab has a small width in the y direction. We can approximate the volume under the function graph by adding up the volumes of the slabs, a calculation which is equivalent to the summation of an integral. As the number of slabs approaches infinity (and their width becomes infinitessimally small), the summation of the integral becomes an integral of an integral.

x-constant slabs work in the same way, but the order is switched -- a manifestation of Fubini's Theorem.

In this demo, you have the option of viewing the x-constant and y-constant slabs for a function f(x, y). You can vary the number of slabs by changing "xRes" and "yRes".