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Why the difference?

• To: mathgroup@smc.vnet.net
• Subject: [mg10760] Why the difference?
• From: Ram Kochhar <rameric@eskimo.com>
• Date: Mon, 2 Feb 1998 00:44:56 -0500
• Organization: Eskimo North (206) For-Ever

Consider the following evaluations
  ans1 = Integrate[Log[x^2+y^2],{x,-1,1},{y-1,1}]
  expr = Log[(x-a)^2 + (y-b)^2]
  ans2 = Integrate[expr,{x,-1,1},{y,-1,1}] /. {a->0,b->0}
  ans3 = Integrate[expr,{x,-1,,a,1},{y,-1,b,1}] /. {a->0,b->0}

Mathematica gives different results.  Difference is probably due to
branch cuts.
Is there a way to calculate these so that mathematica  gives same
result?  I am
interested in near field interactions of Newtonian potentials.  I could
subdivide
the domain of integration in this particular case. But is there another
way?

                                                             Ram kochhar

rameric@eskimo.com