Re(2): Re: Re: integration problem
- To: mathgroup at smc.vnet.net
- Subject: [mg16380] Re(2): [mg16319] Re: [mg16264] Re: integration problem
- From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
- Date: Thu, 11 Mar 1999 02:16:49 -0500
- Sender: owner-wri-mathgroup at wolfram.com
On Mon, Mar 8, 1999, Ersek, Ted R <ErsekTR at navair.navy.mil> wrote:
>Andrzej Kozlowski wrote:
>
>-----------------------------------
>Mathematica can actually compute this integral, and even gets the right
>answer, provided the package <<Calculus`Limit` is loaded.
>
>In[2]:=
><<Calculus`Limit`
>
>In[3]:=
>FullSimplify[Integrate[1/(2*x + Sqrt[3*x + 1]), {x, 0, 1}]]
>Out[3]=
> 2 3/5
>Log[2 (-) ]
> 3
>
>However, unless the Limit package is loaded Mathematica can't calsulate
>the limit of this last expre4ssion as x->1. It is usually a good idea to
>load in the Limit package in such type of situation.
>
>-----------------------------
>
>There are a number of cases where the Limit package gives the wrong answer.
>I think you still have to proceed with caution. I would only try the
>approach above if I wasn't satisfied with the result when I didn't use the
>Limit package.
>
>Regards,
>Ted Ersek
>
I am not quite sure what exactly you mean. Sure, there are bugs in the
Limit package. But I do not know of any case when Mathematica gives the
right answer without the Limit package loaded but a wrong answer after
the package has been loaded. If such a case exists than you are of course
right and one should adopt the policy you recommend. But if not, in other
words if your only risk is that you might get a wrong answer in
situations in which Mathematica alone would give you no answer or perhaps
also a wrong answer, than the only implication seems to be that you
should never trust any answer you get using Mathematica which involves
limits. But that is always the case, not only with Mathematica but all
symbolic math programs. Fortunately the correctness of such answers is
usually easy to test, either by using NIntegrate in cases like this one
or by looking at suitable tables of values in other cases involving
limits. So I would recommend loading in the Limit package and then always
checking the answers you get by independent means.
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp/
http://eri2.tuins.ac.jp/