       Integrate a Piecewise funition, stange behaviour

• To: mathgroup at smc.vnet.net
• Subject: [mg53799] Integrate a Piecewise funition, stange behaviour
• From: rik <rikypi_CREPA_SPAMMONE at libero.it>
• Date: Fri, 28 Jan 2005 02:43:42 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```hi,
i must evaluate this Integrate[]:

int1 = Integrate[f,  {w, - \[Infinity], \[Infinity]}]

where:

f = Piecewise[
{{2/355, Inequality[2, LessEqual, w, LessEqual, 8] &&
Inequality[4, LessEqual, w + w, LessEqual, 12] &&
Inequality[5, LessEqual, w + w, LessEqual, 10] && w
â?¥ 0 && w â?¥ 0}}, 0]

if i try to evaluate int, Mathematica (ver 5.1) takes 500-600 Mbyte of
ram and, after hours and hours, not arrives to any result :-(

But if i apply Reduce to domain like this:

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

and then i try to evaluate the follow command:

Integrate[2/355 Boole[red1],  {w, - \[Infinity], \[Infinity]}]

Mathematica do the calculation in few seconds!!!

Why this behaviour?

The two expression, f and "2/355 Boole[red1]", are not equal for the
Kernel of Mathematica?

Is there a way to predict the complexity of a integral of a Piecewise
function?

thanks and SORRY for my english

Riccardo Piovosi

```

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