Re: Re: Integrate a Piecewise funition, stange behaviour

• To: mathgroup at smc.vnet.net
• Subject: [mg53870] Re: [mg53851] Re: Integrate a Piecewise funition, stange behaviour
• From: DrBob <drbob at bigfoot.com>
• Date: Tue, 1 Feb 2005 04:08:20 -0500 (EST)
• References: <200501280743.CAA00286@smc.vnet.net> <ctfvgo\$pi8\$1@smc.vnet.net> <200501300818.DAA08819@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Both integrals evaluate almost instantly in version 5.1:

f=Piecewise[{{2/355,Inequality[
2,LessEqual,w[2],LessEqual,8]&&Inequality[4,LessEqual,w[2]+w[3],
LessEqual,12]&&Inequality[5,
LessEqual,w[1]+w[2],LessEqual,10]&&w[1]â?¤0&&w[3]â?¤0}},0];
int1=Integrate[f,{w[2],-Infinity,Infinity}]

Piecewise[{{(2/355)*(3 + w[1]),
(-3 < w[1] < -2 && w[1] - w[3] < 1 &&
w[3] <= 0) || (-2 <= w[1] <= 0 &&
w[1] - w[3] <= 1 && w[3] <= 0)},
{(2/355)*(4 + w[3]),
(w[3] > -4 && -3 < w[1] < -2 &&
w[1] - w[3] >= 1) || (w[3] > -4 &&
-2 <= w[1] <= 0 && w[1] - w[3] > 1)}}]

red1=Reduce[Inequality[
2,LessEqual,w[2],LessEqual,8]&&Inequality[4,LessEqual,w[
2]+w[3],LessEqual,12]&&Inequality[5,LessEqual,w[1]+
w[2],LessEqual,10]&&w[1]â?¤0&&w[3]â?¤0];

int2=Integrate[(2/355)*Boole[red1],{w[2],-Infinity,Infinity}]

Piecewise[{{6/355, w[1] == 0 &&
-1 <= w[3] <= 0}, {(2/355)*(3 + w[1]),
-3 < w[1] < 0 && w[1] - w[3] < 1 &&
w[3] <= 0}, {(2/355)*(4 + w[3]),
(w[1] == 0 && -4 < w[3] < -1) ||
(-3 < w[1] < 0 && w[3] > -4 &&
w[1] - w[3] >= 1)}}]

Bobby

On Sun, 30 Jan 2005 03:18:12 -0500 (EST), rik <rikypi_CREPA_SPAMMONE at libero.it> wrote:

> DrBob ha scritto:
>> Try posting in InputForm, so that the code isn't so garbled.
>>
>> http://www.eclecticdreams.net/DrBob/copy_as_inputform.htm
>>
>> Bobby
>>
>> On Fri, 28 Jan 2005 02:43:42 -0500 (EST), rik <rikypi_CREPA_SPAMMONE at libero.it> wrote:
>>
>>
>
>
> i've followed the instruction, and this's the result. I hope that source
>
> f = Piecewise[{{2/355, Inequality[2, LessEqual, w[2], LessEqual, 8] &&
> Inequality[4, LessEqual, w[2] + w[3], LessEqual, 12] &&
>       Inequality[5, LessEqual, w[1] + w[2], LessEqual, 10] && w[1] <= 0
> && w[3] <= 0}}, 0]
>
> int1 = Integrate[f, {w[2], -Infinity, Infinity}]
>
> red1 = Reduce[Inequality[2, LessEqual, w[2], LessEqual, 8] &&
> Inequality[4, LessEqual, w[2] + w[3], LessEqual,
>      12] && Inequality[5, LessEqual, w[1] + w[2], LessEqual, 10] && w[1]
> <= 0 && w[3] <= 0]
>
> int2 = Integrate[(2/355)*Boole[red1], {w[2], -Infinity, Infinity}]
>
> thanks a lot!
>
>
>
>

--
DrBob at bigfoot.com
www.eclecticdreams.net

```

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