bythenumbers - Numerical integration

Integration is a smoothing operation, and numerical integration is, in its essence, a stable operation. Many formulas (or rules) exist. The most basic of these is the so-called rectangular rule, which effectively amounts to a Riemann sum with finite n (or, equivalently, fixed T). Perusal of any elementary text on numericaI analvsis would uncover several other classical formulas, such as the trapezoidal rule and Simpson´s rule. Some other rules include the midpoint rule, the corrected trapezoidal rule, Tick´s rule, Simpson´s three-eighths rule, and Bodes rule.