Re: Multiple integration: bug?

*To*: mathgroup at smc.vnet.net*Subject*: [mg122418] Re: Multiple integration: bug?*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Fri, 28 Oct 2011 05:33:33 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201110262141.RAA00170@smc.vnet.net>*Reply-to*: drmajorbob at yahoo.com

You can also "automate" the Integral as follows: n = 8; xvec = Flatten@{0, Array[x, n]}; limits = Thread[{Rest@xvec, Most@xvec, 1}]; Integrate[1, Sequence @@ limits] 1/40320 Bobby On Thu, 27 Oct 2011 05:28:02 -0500, Heike Gramberg <heike.gramberg at gmail.com> wrote: > What version are you using? On Mathematica 8.0.1 I get the right answer > (1/720) with your code. > > BTW, you could also do something like this to calculate the integral; > > Integrate[1, {x[1], 0, 1}, {x[2], x[1], 1}, {x[3], x[2], 1}, {x[4], > x[3], 1}, {x[5], x[4], 1}, {x[6], x[5], 1}] > > Heike. > > > > On 26 Oct 2011, at 23:41, Dr. Wolfgang Hintze wrote: > >> In calculating Integrals of the type Integrate[0<x1<x2<...<xn<1] which >> should give 1/n! I observed a strange behaviour >> >> Using UnitStep[] it works fine for n=2 to n=5: >> >> In[48]:= >> Integrate[UnitStep[x[2] - x[1]]*UnitStep[x[3] - x[2]]*UnitStep[x[4] - >> x[3]]*UnitStep[x[5] - x[4]], {x[1], 0, 1}, {x[2], 0, 1}, {x[3], 0, 1}, >> {x[4], 0, 1}, {x[5], 0, 1}] >> Out[48]= >> 1/120 >> >> >> It gives nonsense for n=6 (and higher): >> >> In[47]:= >> Integrate[UnitStep[x[2] - x[1]]*UnitStep[x[3] - x[2]]*UnitStep[x[4] - >> x[3]]*UnitStep[x[5] - x[4]]*UnitStep[x[6] - x[5]], {x[1], 0, 1}, {x[2], >> 0, 1}, {x[3], 0, 1}, {x[4], 0, 1}, {x[5], 0, 1}, >> {x[6], 0, 1}] >> Out[47]= >> -(1/4) >> >> Is this a bug or did I make a mistake somewhere (did not consider >> bounds or depth level etc.)? >> >> Any comment is appreciated. >> >> BTW: using Boolean instead of UnitStep seems to have no restriction. >> >> --- Wolfgang >> >> > > -- DrMajorBob at yahoo.com

**References**:**Multiple integration: bug?***From:*"Dr. Wolfgang Hintze" <weh@snafu.de>