Date: Dec 11, 2012 2:24 AM
Author: Alex Krasnov
Subject: definite double integral issue

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.