The Double Integral      

The double integral is defined to be the limit of a double Riemman Sum.  It is this definition that is used most widely in applications, and as we shall see below, the definition is critical to understanding and utilizing the double integral.  Moreover, a double integral over a type I or type II region reduces to either a type I or a type II iterated integral, thus allowing us--and often Maple, as well--to evaluate double integrals.  Before we begin, let's load some packages.

>	restart:with(plots):with(plottools):with(VectorCalculus):

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The Double Integral

Volumes by Parallelpipeds (Boxes Instead of Slices)

Changing from a Type I to a Type II integral (or vice versa)

Exercises