Re: Incorrect symbolic improper integral
- To: mathgroup at smc.vnet.net
- Subject: [mg103645] Re: [mg103586] Incorrect symbolic improper integral
- From: Curtis Osterhoudt <cfo at lanl.gov>
- Date: Thu, 1 Oct 2009 06:38:47 -0400 (EDT)
- Organization: LANL
- References: <30167826.1254225639354.JavaMail.root@n11> <200909300903.FAA09670@smc.vnet.net>
- Reply-to: cfo at lanl.gov
Yes, Jason is obviously using 7.0.0. I use that version on a linux machine, and get what he reported. Wolfram|Alpha also gets Pi/E -- they need to update their version! > From: jwmerrill at gmail.com [mailto:jwmerrill at gmail.com] > > > Below is a definite integral that Mathematica does incorrectly. > Thought someone might like to know: > > In[62]:= Integrate[Cos[x]/(1 + x^2), {x, -\[Infinity], \[Infinity]}] > > Out[62]= \[Pi]/E > > What a pretty result--if it were true. The correct answer is \[Pi]*Cosh > [1], which can be checked by adding a new parameter inside the > argument of Cos and setting it to 1 at the end: > > In[61]:= Integrate[Cos[a x]/(1 + x^2), {x, -\[Infinity], \[Infinity]}, > Assumptions -> a \[Element] Reals] > > Out[61]= \[Pi] Cosh[a] > > Regards, > > Jason Merrill > > > > -- ================================== Curtis Osterhoudt cfo at remove_this.lanl.and_this.gov PGP Key ID: 0x4DCA2A10 ==================================
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