NIntegrate - Gaussian quadrature more exact than thought

*To*: mathgroup at smc.vnet.net*Subject*: [mg73833] NIntegrate - Gaussian quadrature more exact than thought*From*: "janos" <janostothmeister at gmail.com>*Date*: Thu, 1 Mar 2007 06:23:13 -0500 (EST)

NIntegrate[x^4, {x, 0, 1}, Method->GaussKronrod, GaussPoints->2] gives 0.2, the exact result, although the Gauss quadrature should be inexact on a polynomial of degree 2n+2 where n is the number of GaussPoints. More exactly, we expected the same results as here: << NumericalMath`GaussianQuadrature` gw = GaussianQuadratureWeights[2, 0, 1] f[{x_, y_}] := x^4 y Total[f /@ gw] 0.194444 This is inexact, OK. Why is NIntegrate so good? Something I may have missed. Thank you for your help. Janos