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

*To*: mathgroup at smc.vnet.net*Subject*: [mg71978] Re: How can I get this spiked Integral evaluated???*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Thu, 7 Dec 2006 06:25:20 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*References*: <el687j$2pv$1@smc.vnet.net>

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. > Do you have any particular reason for not doing a symbolic integration (returning an exact result) first, then asking for a numeric result to any precision you might want? In[1]:= Integrate[Exp[-x^2], {x, -900, 1000}] Out[1]= 1 - Sqrt[Pi] (Erf[900] + Erf[1000]) 2 In[2]:= N[%] Out[2]= 1.77245 In[3]:= N[%%, 30] Out[3]= 1.77245385090551602729816748334 Regards, Jean-Marc