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 For Mathematica related links and resources try: <http://www.sstreams.com/Mathematica/>