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