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MathGroup Archive 2000

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Re: Integrate[(1 - Exp[-kel*t]), {t, 0, Infinity]?=-1/kel

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24432] Re: [mg24383] Integrate[(1 - Exp[-kel*t]), {t, 0, Infinity]?=-1/kel
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Tue, 18 Jul 2000 00:58:30 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

on 7/13/00 12:13 PM, GyA Csanady at csanady at gsf.de wrote:

> Dear MathGroup,
> I integrated the function (1 - Exp[-kel*t]) between zero and Infinity by
> using Mathematica 4 and assuming that kel is positiv:
> 
> Integrate[(1 - Exp[-kel*t]), {t, 0, Infinity}, Assumptions -> kel > 0]
> 
> Mathematica resulted in a finite integral being ?1/kel.
> 
> This result is obviously wrong since the function investigated does not
> have a finite integral. However I am not sure what is wrong.
> Any help will be appreciated.
> With best regards
> Gy. Csanady
> 


This looks to me like another bug in Integrate. (In general Integrate is
very unreliable for functions with parameters and the Assumptions mechanism
is so weak and buggy as to be virtually useless). You will get the same
answer whether you include the constant term 1 or not (it seems to be
ignored by Mathematica so that the answer is the same , for example, for
Integrate[(3 - Exp[-kel*t]), {t, 0, Infinity}, Assumptions -> kel > 0] and
so on.).

On the other hand, the integral is divergent whether you make any
assumptions on kel or not, and Mathematica correctly tells you that if you
evaluate:

In[29]:=
Limit[Integrate[(1 - Exp[-kel*t] ), {t, 0, p}] // Simplify, p -> Infinity]
Out[29]=
Infinity

(this doesn't work without Simplify)

Andrzej
-- 
Andrzej Kozlowski
Toyama International University, JAPAN

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