The strange behaviour of NIntegrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg53508] The strange behaviour of NIntegrate*From*: Zaeem Burq <Z.Burq at ms.unimelb.edu.au>*Date*: Sat, 15 Jan 2005 01:44:07 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

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

**Follow-Ups**:**Re: The strange behaviour of NIntegrate***From:*DrBob <drbob@bigfoot.com>

**Re: The strange behaviour of NIntegrate***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>