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Re: Bug in Integrate?

• To: mathgroup at smc.vnet.net
• Subject: [mg28770] Re: Bug in Integrate?
• From: "Paul Lutus" <nospam at nosite.com>
• Date: Sat, 12 May 2001 01:36:39 -0400 (EDT)
• References: <9dhuev$kn4@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

"Wil Kortsmit" <rcwil at win.tue.nl> wrote in message
news:9dhuev$kn4 at smc.vnet.net...
> Dear Mathematica Group,
>
> I am a very enthusiastic Mathematica user.
> Mathematica has become faster, but what I like more is reliable
integration.
> In Mathematica 4.1 evaluating the expression
>
> Integrate[Abs[x^4 - 4x^3 + 2x^2 + 1], {x, 0, 4}]
>
> gives me -14/5 as the result, what of course can not be correct.
> Or am I overlooking something?

I *think* this odd result arises from the fact that Abs[] doesn't process
symbolic expressions, returning them unchanged, and Integrate is seeking a
symbolic result if possible, so it may not deal with Abs[] as one would
expect. By contrast, this approach:

NIntegrate[Abs[f[x]], {x, 0, 4},MaxRecursion->16]

Produces:

23.5293

I may be wrong about this, but I think it is correct.

--
Paul Lutus
www.arachnoid.com