another integral problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg32577] another integral problem*From*: Bradley Stoll <BradleyS at Harker.org>*Date*: Wed, 30 Jan 2002 03:18:50 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

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