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MathGroup Archive 2006

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Re: How can I get this spiked Integral evaluated???

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72000] Re: [mg71957] How can I get this spiked Integral evaluated???
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Thu, 7 Dec 2006 06:26:20 -0500 (EST)
  • Reply-to: hanlonr at cox.net

Integrate[Exp[-x^2], {x, -900, 1000}]

(1/2)*Sqrt[Pi]*(Erf[900] + Erf[1000])

%//N

1.77245

NIntegrate[Exp[-x^2], {x, -900, 1000},WorkingPrecision->65,MaxRecursion->15]

1.7724538509055160272981674833411451827975494561223871282


Bob Hanlon

---- Zeno <zeno333 at mindspring.com> wrote: 
> This is an integral with a spike that is not in the middle of the
> integral range. Here is the integral...
> 
> NIntegrate[Exp[-x^2], {x, -900, 1000}]
> 
> Mathemtaica 5.2.2 gives this error message....
> 
>  "Numerical \integration stopping due to loss of precision. Achieved
> neither the requested \PrecisionGoal nor AccuracyGoal; suspect one of
> the following: highly \oscillatory integrand or the true value of the
> integral is 0. If your \integrand is oscillatory on a (semi-)infinite
> interval try using the option \Method->Oscillatory in NIntegrate. 
> MoreÅ 
> 
> However, to use the option "Method->Oscillatory" one of the bounds of
> the integral must be infinity, so that would not work here. How do I
> get it to to the integral in the range -900 to 1000??
> The correct answer is 1.77245.
> 


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