Date: Dec 11, 2012 7:54 PM
Author: Murray Eisenberg
Subject: Re: definite double integral issue
Yes, Mathematica has always (?) supported such dependent bounds in iterated integrals.

Both versions of your input work just fine in Mathematica 9.0.0 under both Mac OS X 10.8.2 and Windows 7, the second returning result:

-0.741019

I cannot imagine why you would get a kernel crash with this in 8.0.4.

On Dec 11, 2012, at 2:26 AM, Alex Krasnov <akrasnov@eecs.berkeley.edu> wrote:

> 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]+S qrt[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

---

Murray Eisenberg murray@math.umass.edu

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