Newton-Cotes Formulas

Numerical Analysis · Axiom Academy

A unified family of integration formulas based on polynomial interpolation All Newton-Cotes formulas follow the same pattern: Sample the function at n+1 equally-spaced points Build an interpolating polynomial of degree n through these points Integrate the polynomial exactly Each value of n gives a different formula: Closed formulas include the endpoints (what we've seen so far). Open formulas exclude the endpoints—useful when f(a) or f(b) is undefined! A formula has degree of precision d if it integrates all polynomials of degree ≤ d exactly. 5. Why Not Use High-Order Formulas? It seems like using more points should always be better... but there's a catch!

This is the written version of the interactive lesson above. See the full Numerical Analysis course.