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