       Re: Integrating using If[ ]

• To: mathgroup at smc.vnet.net
• Subject: [mg33323] Re: [mg33301] Integrating using If[ ]
• From: "Philippe Dumas" <dumasphi at noos.fr>
• Date: Thu, 14 Mar 2002 19:51:26 -0500 (EST)
• References: <200203140722.CAA10975@smc.vnet.net>
• Reply-to: "Philippe Dumas" <dumasphi at noos.fr>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Michael

Try this:
x[t_] = Exp[-Abs[t]]

If[t>=0,Exp[-t],Exp[t]];

And then you get the result with :
f[s_] = Integrate[x[t] Exp[-s t], {t, -Infinity, Infinity}]

Philippe Dumas
99, route du polygone
03 88 84 67 80
67100 Strasbourg

----- Original Message -----
From: "Michael Chang" <michael_chang86 at hotmail.com>
To: mathgroup at smc.vnet.net
Subject: [mg33323] [mg33301] Integrating using If[ ]

> Hi everyone,
>
> While recently trying out my spiffy new version of Mathematica 4.1 for
> Windoze XP, I've stumbled upon the following perplexing result.
>
> Suppose I define
>
> In:= x[t_]:=If[t>=0,Exp[-t],Exp[t]];
>
> If I now try and evaluate (a two-sided Laplace Transform)
>
> In:= Integrate[x[t] Exp[-s t],{t,-Infinity,Infinity}]
>
> all I get back is essentially an unevaluated answer.  Replacing
> {-Infinity, Infinity} by, for instance, {-100,100}, *does* give me an
>
> Typing in
>
> In:= Integrate[Exp[-Abs[t]] Exp[-s t],{t,-Infinity,Infinity}]
>
> however, does give me back a meaningful result with the conditionals
> properly stated that -1<Re[s]<1.  Why does In work, but not In
> and In?  Am I foolishly doing something stup!d here?
>
> Michael
>
>

```