Simpson Integration Rules Fast Derivation with B-Splines

Simpson Integration Rules

Fast Derivation with B-Splines

(including partial integrals)

Charles O'Neill

29 October 2010

The 3 and 4 point Simpson rules numerically integrate equally-spaced discrete data values. The 4 point rule is typically named Simpson's 3/8 rule. This short note describes an interesting and fast derivation of Simpson's  rules including the associated partial integrals. Non-multiple data point integration is discussed in a surprising finale to Simpson's 3/8ths rule.

The full derivation is available here.