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