Double Integral on Rectangular Region


Illustration of the planar slices that are added up (integrated) to give the volume under a surface. A is a small volume dx thick with a surface area of integral of which can be evaluated at any location. By then integrating from to the volumes made by multiplying the integrated area and the thickness, , the full volume can be obtained. The direction of the slices can be switched and the final volume should be the same provided is continuous throughout the region.