a Double Intergral of a function f(x,y) in the bounded region D is the sum of the products of the function f(xi,yi) with the area of the largest partitioned rectangle of the region D as the area of the largest partitioned rectangle goes to zero.

a Triple intergral of a function f(x,y,z) in the bounded region D is the sum of the products of the function f(xi,yi,zi) with the volume of the largest partitioned rectangle of the region D as the volume of the largest partitioned rectangle goes to zero.