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[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
>
>

```

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