Abstract
ABSTRACT Every freshman calculus textbook contains a section on numerical integration in which the trapezoidal rule and Simpson's rule are introduced. Although there are several ways to establish each of these numerical methods of integration, every textbook I have encountered (in choosing the path of least resistance) establishes the trapezoidal rule in essentially the same way—using the well-known formula for the area of a trapezoid. (For example, see [3].) Things are not quite the same with Simpson's rule, however, as almost any method of establishing it requires some work. Thus, if possible, one should establish Simpson's rule using a method that does more than just establish Simpson's rule. And I have an idea on that!
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