       Re: Multiple integration: bug?

• To: mathgroup at smc.vnet.net
• Subject: [mg122375] Re: Multiple integration: bug?
• From: Heike Gramberg <heike.gramberg at gmail.com>
• Date: Thu, 27 Oct 2011 06:28:02 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201110262141.RAA00170@smc.vnet.net>

```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, 0, 1}, {x, x, 1}, {x, x, 1}, {x, x, 1},  {x, x, 1}, {x, x, 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:=
> 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
>
>

```

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