Re: What is wrong?
- To: mathgroup at smc.vnet.net
- 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 wolfram.com
> 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 scisun.sci.ccny.cuny.edu
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