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Re: Re: Incorrect symbolic improper integral

• To: mathgroup at smc.vnet.net
• Subject: [mg103692] Re: [mg103645] Re: [mg103586] Incorrect symbolic improper integral
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Fri, 2 Oct 2009 08:26:03 -0400 (EDT)
• References: <30167826.1254225639354.JavaMail.root@n11>
• Reply-to: drmajorbob at yahoo.com

> Wolfram|Alpha also gets Pi/E -- they need to update their version!
>

No... Pi/E is correct, as other posts have pointed out.

Bobby

On Thu, 01 Oct 2009 05:38:47 -0500, Curtis Osterhoudt <cfo at lanl.gov> wrote:

>   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
>>
>>
>>
>>
>
>


-- 
DrMajorBob at yahoo.com