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. >