The trapezoidal rule gives us a crude technique to approximate the integral on a given interval [a, b]. This technique reduces to finding the area of the trapezoid shown in Figure 1.
Figure 1. The trapezoidal rule applied to integrating on the interval [0, 1].
One problem with this technique is that we cannot iterate it to find a better answer. In other topics, we will look at other ways of finding better approximations to the integral using modifications of this technique.
Useful background for this topic includes:
- Bradie, Section 6.4, General Newont-Cotes Formulas, p.456.
- Mathews, Section 7.1, Introduction to Quadrature, p.355.
- Weisstein, http://mathworld.wolfram.com/TrapezoidalRule.html.
Copyright ©2005 by Douglas Wilhelm Harder. All rights reserved.