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MathGroup Archive 1997

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Re: What is wrong?

  • To: mathgroup at
  • Subject: [mg7707] Re: [mg7696] What is wrong?
  • From: David Withoff <withoff>
  • Date: Wed, 2 Jul 1997 14:21:27 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

> In[1]:= Integrate[x*Sin[x]/(x^2+1),{x,0,Infinity}]
>         Pi
> Out[1]= ---
>         2 E
> In[2]:= f[x_] = Evaluate[ Integrate[x*Sin[x]/(x^2+1),x]] ;
> In[3]:= ans = f[Infinity] - f[0]
>         E Pi
> Out[3]= ----
>          2
> In[4]:= $Version
> Out[4]= DEC OSF/1 Alpha 2.2 (September 9, 1994)
> sergio
> E-mail: sergio at

Simply substituting Infinity for x in the indefinite integral,
as in f[Infinity], won't work for computing the limit of the
indefinite integral at Infinity.  Infinity+I evaluates to Infinity,
which is in this example treated as a real infinity, thereby losing
some information that is needed for computing the limit.  The
Integrate function computes this limit correctly for the definite
integral, and so gets a correct answer.  The indefinite integral
is also correct, and with correct limits will give a correct
value for the definite integral.

Dave Withoff
Wolfram Research

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