ABSTRACT
In this chapter, we develop the integral for functions of n variables. The theory in the general case follows the same lines as for n = 1 and we therefore begin with a review of integration of functions of one variable. Because of the complexity of notation, we also treat separately the case n = 2 before proceeding to the general case. After developing some of the properties of the integral, we show that all continuous functions and even some discontinuous functions are integrable. We note that the sections defining the integral are particularly important, since the integral often arises in practical applications as a limit of the sorts of sums found in the definition of the integral.
