Re: definite double integral issue

*To*: mathgroup at smc.vnet.net*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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20121211072625.7673968A8@smc.vnet.net> <20121212005637.8C318690B@smc.vnet.net>

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 > > > > > >

**References**:**definite double integral issue***From:*Alex Krasnov <akrasnov@eecs.berkeley.edu>

**Re: definite double integral issue***From:*Murray Eisenberg <murray@math.umass.edu>