When [math]f\left(x,y\right)[/math] is a positive function over a rectangular region [math]R[/math] in the [math]xy[/math]-plane, we may interpret the double integral of [math]f[/math] over [math]R[/math], that is [math]\int\int_Rf\left(x,y\right)dA[/math], as the volume of the 3-dimensional solid region bounded below by [math]R[/math] and above by the surface [math]z=f\left(x,y\right)[/math].

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]