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.

# Background

Useful background for this topic includes:

- 3. Lagrange Interpolation
- 7 Taylor Series (error analysis)

# References

- 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.