Re : Principal Value integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg52373] Re : [mg52361] Principal Value integral*From*: "Jaccard Florian" <Florian.Jaccard at he-arc.ch>*Date*: Thu, 25 Nov 2004 05:49:44 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hello Carlo, I obtain the correct answer with 5.0 ! What version do you use? In fact, we always should be very prudent using Integrate, because there are still a lot of bugs. Just look in the archive! A good thing is always to check that NIntegrate gives the same numerical value! Regards F.Jaccard -----Message d'origine----- De : Carlo Teubner [mailto:AskMeAndIllTellYou. at example.com] Envoyé : mercredi, 24. novembre 2004 08:33 À : mathgroup at smc.vnet.net Objet : [mg52361] Principal Value integral The following Principal Value integral does not appear to give the correct result. Integrate[1/(x^3-1), {x, -Infinity, Infinity}, PrincipalValue->True] This gives I Pi / 3, which surely can't be right since the answer should be real. When doing it numerically, it gives the right answer: <<NumericalMath`CauchyPrincipalValue` CauchyPrincipalValue[1/(x^3-1), {z, -Infinity, {1}, Infinity}] This gives -1.8138 which is the correct answer (it's -Pi/Sqrt[3]). Any explanations? Is this a bug or am I missing something? Carlo