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Topic: definite double integral issue
Replies: 3   Last Post: Dec 13, 2012 4:07 AM

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 Alex Krasnov Posts: 15 Registered: 10/3/12
Re: definite double integral issue
Posted: Dec 13, 2012 4:07 AM

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@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
> Mathematics & Statistics Dept.
> Lederle Graduate Research Tower phone 413 549-1020 (H)
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>
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>

Date Subject Author
12/11/12 Murray Eisenberg
12/13/12 Alex Krasnov