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big imaginary error in region integration

• To: mathgroup at smc.vnet.net
• Subject: [mg48075] big imaginary error in region integration
• From: o.soloviev at ewi.tudelft.nl (Oleg Soloviev)
• Date: Tue, 11 May 2004 05:19:57 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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.

• Follow-Ups:
  • Re: big imaginary error in region integration
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>