Introduction to Double Integrals

Double integrals are fundamental tools in multivariable calculus for computing volumes under surfaces defined by functions of two variables. While single-variable integration calculates the area under a curve, double integrals extend this concept to evaluate the volume between a surface and a planar region. This generalization is particularly va...

A double integral gives the volume under a surface defined by a function of two variables over its domain, shown as the region in the plane.

Consider an excavation site defined by a rectangular region on the xy-plane. Above this region lies a surface whose height represents the ground elevation.

The total volume of soil to be ...