The surface integral of some function f(x, y, z) over the graph of a function g(x, y) is illustrated here. One window shows the "shingles" of g(x, y), colored according to the value of f(x, y, z), and the second displays the value of the integral as the volume above the x-y plane minus the volume below the x-y plane. Note that each rectangular prism in this second window has a base equivalent in area to that of a corresponding shingle in the first window, and a height corresponding to the value of f(x, y, z) for that shingle.