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