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Re: Another strange bug in Mathematica 4.0's Integrate
*To*: mathgroup at smc.vnet.net
*Subject*: [mg25339] Re: Another strange bug in Mathematica 4.0's Integrate
*From*: Richard Fateman <fateman at cs.berkeley.edu>
*Date*: Sat, 23 Sep 2000 03:36:04 -0400 (EDT)
*Organization*: University of California, Berkeley
*References*: <8q21lp$hoh@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
One could argue that your assignment of wrong and correct is
reversed.
Here is the argument:
Either integral would be +-Pi r^2/2. It depends on the sign
of the Sqrt inside the integral.
The first answer, Out[1] encodes the + and - solution.
The second answer gives only one solution, and so is
incomplete.
I wouldn't necessarily endorse this argument, but it is
independent of your "path" observation below.
RJF
Hendrik van Hees wrote:
>
> Here you see another strange bug in Integrate.
>
> In[1]:= Integrate[Sqrt[(r-x)(r+x)],{x,-r,r},Assumptions->{r>0}]
>
> 2
> Pi r Sqrt[r ]
> Out[1]= ------------- (WRONG)
> 4
>
> while
>
> In[2]:= Integrate[Sqrt[r^2-x^2],{x,-r,r},Assumptions->{r>0}]
>
> 2
> Pi r
> Out[2]= ----- (correct)
> 2
>
> and please don't tell me that there is an ambiguity concerning the path
> of integration in the complex plane. It is very clear that the integral
> is meant to be taken along the real axis from -r to r, because if
> Integrate would be a complex path integral the user should be able to
> specify this path of integration!
>
> --
> Hendrik van Hees Phone: ++49 6159 71-2751
> c/o GSI-Darmstadt SB3 3.183 Fax: ++49 6159 71-2990
> Planckstr. 1 mailto:h.vanhees at gsi.de
> D-64291 Darmstadt http://theory.gsi.de/~vanhees/index.html
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