Re: The strange behaviour of NIntegrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg53519] Re: [mg53508] The strange behaviour of NIntegrate*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sat, 15 Jan 2005 21:07:47 -0500 (EST)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

I get a real result. $Version 5.1 for Mac OS X (October 25, 2004) ?[x_]:=1/(E^(x^2/2)*Sqrt[2*Pi]); K[s_]:=((1-Sqrt[s])*?[(1-Sqrt[s])/Sqrt[1-s]])/(1-s)^1.5`; NIntegrate[K[s],{s,0,1}] 0.420616 However, use Chop NIntegrate[K[s],{s,0,1}] // Chop or try using (3/2) instead of 1.5` in the definition of K Bob Hanlon > > From: Zaeem Burq <Z.Burq at ms.unimelb.edu.au> To: mathgroup at smc.vnet.net > Date: 2005/01/15 Sat AM 01:44:07 EST > To: mathgroup at smc.vnet.net > Subject: [mg53519] [mg53508] The strange behaviour of NIntegrate > > > Dear all, > > I'll describe the problem briefly first as follows: > > I am trying to NIntegrate a nice function (which I know is integrable), of > the form > > K[s] = h[s]/[(1-s)^1.5] from 0 to 1. > > The function is real, but Mathematica spits out a COMPLEX answer!! > Admittedly, the complex part is very small, and if I truncate the integral > just below 1, the complex bit disappears and changes the real part very > slightly. > > It seems obvious that Math'ca is choosing the last s value just beyond 1, > producing the Sqrt of a negative number in the denominator. > > If interested, here are the calculations and results. Read on if you think > you can help. Thanx. > > \!\(\(\[CurlyPhi][ > x_] := \[ExponentialE]\^\(\(-x\^2\)/2\)\/\@\(2 \[Pi]\);\)\n > \(K[s_] := \(\(\ \)\(\((1 - \@s)\)\ \[CurlyPhi][\(1 - \@s\)\/\@\(1 - > s\)]\)\ > \)\/\((1 - s)\)\^1.5`;\)\) > > NIntegrate[K[s], {s, 0, 1}] > > gives \!\(\(\(0.4206155890394436`\)\(\[InvisibleSpace]\)\) - > 3.304807577181973`*^-49\ \[ImaginaryI]\) > > and > > NIntegrate[K[s], {s, 0, .999999}] > > results in > > 0.420217 > > Any thoughts? > > Zaeem. > > > Zaeem Burq > PhD Stochastic Processes, > Dept. of Mathematics and Statistics, > Unimelb. > > Room 201, Richard Berry Building > University of Melbourne, > Parkville, VIC 3052. > > ph: 8344 4248. > > http://www.ms.unimelb.edu.au/~zab > >