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

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Murray Eisenberg

Posts: 2,105
Registered: 12/6/04
Re: definite double integral issue
Posted: Dec 11, 2012 7:54 PM
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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:


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 <> 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
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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