Re: The strange behaviour of NIntegrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg53527] Re: [mg53508] The strange behaviour of NIntegrate*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sat, 15 Jan 2005 21:08:01 -0500 (EST)*References*: <200501150644.BAA25316@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 15 Jan 2005, at 07:44, Zaeem Burq wrote: > > 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 > > This is completely normal and is exactly what Chop is for: $B&U(B[x_] := 1/(E^(x^2/2)*Sqrt[2*Pi]); K[s_] := ((1 - Sqrt[s])*$B&U(B[(1 - Sqrt[s])/Sqrt[1 - s]])/ (1 - s)^1.5; Chop[NIntegrate[K[s], {s, 0, 1}]] 0.4206155890394436 Andrzej Kozlowski Chiba, Japan http://www.akikoz.net/~andrzej/ http://www.mimuw.edu.pl/~akoz/

**References**:**The strange behaviour of NIntegrate***From:*Zaeem Burq <Z.Burq@ms.unimelb.edu.au>