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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
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