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. >