Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2005
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2005

[Date Index] [Thread Index] [Author Index]

Search the Archive

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
> 
> 


  • Prev by Date: Re: The strange behaviour of NIntegrate
  • Next by Date: Re: The strange behaviour of NIntegrate
  • Previous by thread: Re: The strange behaviour of NIntegrate
  • Next by thread: Colored Surface