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Integrating using If[ ]

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  • Subject: [mg33301] Integrating using If[ ]
  • From: michael_chang86 at (Michael Chang)
  • Date: Thu, 14 Mar 2002 02:22:04 -0500 (EST)
  • Sender: owner-wri-mathgroup at

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[1]:= x[t_]:=If[t>=0,Exp[-t],Exp[t]];

If I now try and evaluate (a two-sided Laplace Transform)

In[2]:= 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
answer, though.

Typing in

In[3]:= 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[3] work, but not In[1]
and In[2]?  Am I foolishly doing something stup!d here?


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