Bythenumbers - Numerical integration

Abstract

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.