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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: [mg71994] Re: How can I get this spiked Integral evaluated???
  • From: Joel Storch <jstorch at earthlink.net>
  • Date: Thu, 7 Dec 2006 06:25:59 -0500 (EST)
  • Organization: EarthLink Inc. -- http://www.EarthLink.net
  • References: <el687j$2pv$1@smc.vnet.net>

Since the integrand is even, we can express the integral as the sum 
I1+I2 where
                 I1=2 NIntegrate[Exp[-x^2],{x,0,900}]
                 I2=NIntegrate[Exp[-x^2],{x,900, 1000}]

I2 is less than 100 Exp[-x^2}/.x->900  which is negligible
Mathematica evaluates I1=1.77245

Zeno 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. 
> More?
> 
> 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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