Illustration of the planar slices that are added up (integrated) to give the volume under a surface. [br]A [math]dxSlice[/math] is a small volume dx thick with a surface area of integral of [math]\int_{Ymin}^{Ymax}f\left(x,y\right)dy[/math] which can be evaluated at any [math]x[/math] location. By then integrating from [math]Xmin[/math] to [math]Xmax[/math] the volumes made by multiplying the integrated area and the thickness, [math]dx[/math], the full volume can be obtained.[br]The direction of the slices can be switched and the final volume should be the same provided [math]f(x,y)[/math] is continuous throughout the region.