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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)
• 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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