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MathGroup Archive 2004

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Re: big imaginary error in region integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48091] Re: [mg48075] big imaginary error in region integration
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Thu, 13 May 2004 00:08:17 -0400 (EDT)
  • References: <200405110919.FAA28268@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 11 May 2004, at 18:19, Oleg Soloviev wrote:

> Hi all,
>
> who can explain, why does Mathematica return complex number when
> integrating real integrand? The imaginary part is of the same
> magnitude here as the real one:
> In[1]:=Needs["Calculus`Integration`"]
> In[2]:=Integrate[x Boole[(1/2+x)^2+y^2<1/100.],{x,-1,1},{y,-1,1}]
> Out[2]=-0.015708-0.0160944 I.
> With exact numbers the answer is real:
> In[3]:=Integrate[x Boole[(1/2+x)^2+y^2<1/100],{x,-1,1},{y,-1,1}]
> Out[3]=-Pi/200.
>
> With regards,
> Oleg.
>
>
Just a matter of numerical precision (again):


Integrate[x Boole[(1/2+x)^2+y^2<1/100`20],{x,-1,1},{y,-1,1}]//Chop


-0.015707963268



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