       Re: Multiple integration: bug?

• To: mathgroup at smc.vnet.net
• Subject: [mg122399] Re: Multiple integration: bug?
• From: Ray Koopman <koopman at sfu.ca>
• Date: Thu, 27 Oct 2011 06:32:23 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j89vct\$224\$1@smc.vnet.net>

```On Oct 26, 2:51 pm, "Dr. Wolfgang Hintze" <w... at snafu.de> 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:=
> Integrate[UnitStep[x - x]*UnitStep[x - x]*UnitStep[x -
> x]*UnitStep[x - x], {x, 0, 1}, {x, 0, 1}, {x, 0, 1},
> {x, 0, 1}, {x, 0, 1}]
> Out=
> 1/120
>
> It gives nonsense for n=6 (and higher):
>
> In:=
> Integrate[UnitStep[x - x]*UnitStep[x - x]*UnitStep[x -
> x]*UnitStep[x - x]*UnitStep[x - x], {x, 0, 1}, {x,
> 0, 1}, {x, 0, 1}, {x, 0, 1}, {x, 0, 1},
> {x, 0, 1}]
> Out=
> -(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

Why not just integrate over 0 < x1 < x2 < ... < xn < 1 ?

In:=
f[n_Integer?Positive] := Block[{x}, Integrate[1, Sequence @@
({#2,#1,1}& @@@ Partition[Prepend[Array[x,n],0],2,1]) ] ]

In:= f

Out= 1/720

```

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