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MathGroup Archive 2012

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definite double integral issue

  • To: mathgroup at smc.vnet.net
  • Subject: [mg129065] definite double integral issue
  • From: Alex Krasnov <akrasnov at eecs.berkeley.edu>
  • Date: Tue, 11 Dec 2012 02:26:25 -0500 (EST)
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I discovered the following issue in Mathematica 8.0.4:

In:	Integrate[x/Sqrt[x^2+y^2], {y, -1/2, 3/2}, {x, -1, 1/2-y}]
Out:	(2*Sqrt[5]-2*Sqrt[13]-16*ArcSinh[1/2]-16*ArcSinh[3/2]+Sqrt[2]*ArcSinh[3]+Sqrt[2]*ArcSinh[5])/32

In:	Integrate[x/Sqrt[x^2+y^2], {y, -0.5, 1.5}, {x, -1.0, 0.5-y}]
Out:	(kernel crash)

I have not yet reproduced this issue in Mathematica 9.0.0. I am uncertain 
whether Integrate actually supports dependent bounds and whether the 
evaluation chain is different for exact and approximate real bounds.

Alex



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