WHY SIMPSON'S RULE,

Simpsons quadrature rule derives from a formula for the volume of certain geometrical solids or a formula for areas bounded by straight lines and thirddegree polynomials. It is one of a sequence of progressively more complex rules that apply exactly to progressively higher-degree polynomials. The use of such rules in situations where they are not exact is justified on the basis of theoretical error terms that decrease as the interval of integration is more finely subdivided. The error terms also depend on derivatives, often unknown, of the functions being integrated. Quadrature rules have been sought that are better suited to use in computing machines. This presents several rules that are generally better than Simpsons Rule, considering both accuracy and ease of application. Author