The trapezoidal rule gives us a technique to approximate the
integral on a given interval [*a*, *b*], but we cannot reduce the error because
the error depends on the width of the interval over which we
are integrating.

By dividing the interval [*a*, *b*] into many smaller intervals, and applying
the trapezoidal rule to each, this allows us to find a better approximation the integral.

# Background

Useful background for this topic includes:

- 3. Iteration
- 12.1 Trapezoidal Rule

# References

- Bradie, Section 7.1, Introduction to Quadrature, p.355.
- Mathews, Section 7.2, Composite Trapezoidal and Simpson's Rule, p.364.

Copyright ©2005 by Douglas Wilhelm Harder. All rights reserved.