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John Barber
02/20/03 12:16pm

Hi Folks:

When I give Mathematica (4.1) the following:

Integrate[(x^2) (1 - Exp[-1/x^12]), {x, 0, Infinity}]

it claims the value of the integral is Infinity. I know this to be
false, both from the physical context of the problem, and from
the fact that a quick glance at a graph of the function shows
that it is indeed integrable.
A numerical integration of the function:

NIntegrate[(x^2) (1 - Exp[-1/x^12]), {x, 0, Infinity}]

yields 0.408472. Furthermore, after a change of variables
x -> 1/z, we have the following as an equivalent expression
for the top integral:

Integrate[(1/z^4)(1-Exp[-z^12]),{z,0,Infinity}]

for which mathematica gives a finite, positive answer:

-(1/12)Gamma[-1/4] = 0.408472

Why the does Mathematica assert, wrongly, that the first form
of the integral is divergent?

Thanks!

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Subject (listing for 'Inconsistent results for strange integral')
Author Date Posted
Inconsistent results for strange integral John Barber 02/20/03 12:16pm
Re: Inconsistent results for strange integral Forum Modera... 02/23/03 1:29pm
Re: Inconsistent results for strange integral John Barber 02/24/03 09:01am
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