The Midpoint Rule for Double Integrals

The midpoint rule for a double integral provides a practical method for estimating volume over a rectangular region when the surface height varies continuously. In civil engineering, this method is useful for approximating the amount of soil to be moved when planning a road across uneven terrain. The road footprint is represented as a rectangle ...

In a civil engineering project, a road is planned through mountainous terrain. To estimate the earthwork required, engineers calculate the volume of soil between the existing terrain and the planned road level.

The planned path of the road is modeled as a rectangular region in the xy-plane. A continuous height function represents th...