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Re: Bug in Integrate?

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

"Wil Kortsmit" <rcwil at> wrote in message
news:9dhuev$kn4 at
> Dear Mathematica Group,
> I am a very enthusiastic Mathematica user.
> Mathematica has become faster, but what I like more is reliable
> 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]



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

Paul Lutus

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