Re: Re: Integrate question

*To*: mathgroup at smc.vnet.net*Subject*: [mg82442] Re: [mg82334] Re: Integrate question*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Sat, 20 Oct 2007 05:54:51 -0400 (EDT)*References*: <200710160728.DAA08846@smc.vnet.net> <ff4hpp$k0e$1@smc.vnet.net> <32260915.1192803351856.JavaMail.root@m35>*Reply-to*: drmajorbob at bigfoot.com

> Ok, Mathematica 2.1 was "mindless" here, but why was it considered to be > "wrong"? Because it was wrong. The integral doesn't converge. The Newton-Leibnez rule (second fundamental theorem of integral calculus) doesn't apply, since the antiderivative isn't equal to the integrand on the range. That condition fails at the pole (1/Sqrt[3]), where the antiderivative is neither continuous nor bounded. Integrate didn't "notice" the theorem doesn't apply, so it used it anyway. Bobby On Thu, 18 Oct 2007 03:44:22 -0500, Oskar Itzinger <oskar at opec.org> wrote: > Ok, Mathematica 2.1 was "mindless" here, but why was it considered to be > "wrong"? > > /oskar > > "Andrzej Kozlowski" <akoz at mimuw.edu.pl> wrote in message > news:ff4hpp$k0e$1 at smc.vnet.net... >> >> The reason is that Mathematica 2.1 was wrong and Mathematica 5.2 is >> much more careful and right. What Mathematica 2.1 did here was simply: >> >> Subtract @@ (Integrate[x/(3 x^2 - 1)^3, x] /. {{x -> 1}, {x -> 0}}) >> 1/16 >> >> in other words, it applied the Newton-Leibnitz rule in a mindless >> way. > > > > -- DrMajorBob at bigfoot.com

**References**:**Integrate question***From:*"Oskar Itzinger" <oskar@opec.org>