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MathGroup Archive 2001

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Re: Different Integration Results

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30358] Re: [mg30344] Different Integration Results
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Sun, 12 Aug 2001 02:29:48 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

This looks like  a bug, although Mathematica's Integrate is in general 
unreliable when dealing with non-analytic functions (in the complex 
plane). Fortunately there are usually several different approaches which 
one should use to  confirm the answer. In your case the following two 
both give 1:

In[24]:=
z=Integrate[rho[x],x]

Out[24]=
             19             19            5              5        49 
ArcTan[x]   7
   
18 (-(-----------) - ---------- + ------------ + ----------- - ------------ + - 
ArcTan[2 x])
         12 (-I + x)    12 (I + x)   6 (-I + 2 x)   6 (I + 2 x)        
18        9
-(--------------------------------------------------------------------------------------------)
                                              35 Pi


In[25]:=
Limit[z, x -> Infinity]

Out[25]=
1
-
2

In[11]:=
Limit[z, x -> -Infinity]

Out[11]=
   1
-(-)
   2

Alternatively, the following also gives the right answer:

In[35]:=
Integrate[TrigToExp[rho[x]],{x,-Infinity,Infinity}]

Out[35]=
1


Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/
On Saturday, August 11, 2001, at 04:40  PM, Harald Grossauer wrote:

>
> Hi,
> I have got a problem with the attached notebook. In the last two lines,
> if I use Integrate[ ] the result is 99/35, NIntegrate[ ] says it is
> "1.". Due to the nature of the problem (quantum theory, fourier
> transform) I would expect the result to be 1 exactly. What could cause
> this difference?
> Greetings, Harald
>
>


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