Re: definite double integral issue

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• Subject: [mg129078] Re: definite double integral issue
• From: Alex Krasnov <akrasnov at eecs.berkeley.edu>
• Date: Thu, 13 Dec 2012 04:06:56 -0500 (EST)
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```I have discovered only one such integral so far. However, since it appears
to be fixed in Mathematica 9.0.0, we can consider this issue closed.

Alex

On Tue, 11 Dec 2012, Murray Eisenberg wrote:

> 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 at 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 at math.umass.edu
> Mathematics & Statistics Dept.
> Lederle Graduate Research Tower            phone 413 549-1020 (H)
> University of Massachusetts                               413 545-2838 (W)
> 710 North Pleasant Street                         fax   413 545-1801
> Amherst, MA 01003-9305
>
>
>
>
>
>

```

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