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RE: another integral problem

• To: mathgroup at smc.vnet.net
• Subject: [mg32613] RE: [mg32577] another integral problem
• From: Bradley Stoll <BradleyS at Harker.org>
• Date: Thu, 31 Jan 2002 01:45:47 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Although that was an error on my part (please close off the absolute value
argument with a ]), that was not the problem.  Thanks for catching that,
Dave.  I should do as I suggest my students do, cut and paste instead of
retyping.  

Bradley

-----Original Message-----
From: David Terr [mailto:dterr at wolfram.com]
To: mathgroup at smc.vnet.net
Subject: [mg32613] Re: [mg32577] another integral problem


Bradley Stoll wrote:

> Awhile ago I had a problem with a triple integral.  Now, I've got troubles
> with a single integral.  I'm sure that it has something to do with 'how'
Mathematica
> finds integrals, but if someone could clue me in...
> Integrate[Abs[x^2 Cos[x]-x^3 + x,{x,0,1.1983}] and Integrate[Abs[x^2
> Cos[x]-x^3 + x,{x,0,1.19836].  From appearance, you might guess that these
> should be pretty close.  The first is pos., while the 2nd is neg, even
> though the integrand is non-neg.  FYI, 1.1983 is an approx. to x^2
> Cos[x]=x^3 -x.  What's interesting, is that when you use a 'better'
approx.,
> the result is neg.  Now, with NIntegrate, there is no problem.  Please
> advise.
>
> Bradley Stoll

It looks like you put the brackets for Abs in the wrong place - the closing
bracket
should go after the last x.

David

Mathematica 5.0 for Linux
Copyright 1988-2001 Wolfram Research, Inc.
 -- Motif graphics initialized --

In[1]:= Integrate[Abs[x^2 Cos[x]-x^3+x],{x,0,1.1983}]

Out[1]= 0.549322

In[2]:= Integrate[Abs[x^2 Cos[x]-x^3+x],{x,0,1.19836}]

Out[2]= 0.549322