RE: [Q] error in Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg8777] RE: [mg8750] [Q] error in Integrate*From*: "Richard W. Finley, M. D." <trfin at umsmed.edu>*Date*: Thu, 25 Sep 1997 12:26:11 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Hi This has already been discussed but why do you say it is obviously = wrong? In fact, it is correct. The answer 1/3 is also correct. If you = define Sqrt[(x-y)^2] to be (x-y) for x>y and -(x-y) for x<y then you get = the answer you desire. If you define it to be (x-y) for all x in the = region, then the answer is indeed zero. The problem is that Sqrt is = multiple valued and how you define it in a given region determines the = answer. Mma is somewhat inconsistent in this regard because if you use = NIntegrate you get a different answer than Integrate, but both are = formally correct. One must simply be more precise in the formulation of = the problem. There are always subtle pitfalls waiting for those who = integrate multiple valued functions...I have been "burned" on many = occasions. RF -----Original Message----- From: Denis Barbier [SMTP:barbier at cmapx.polytechnique.fr] To: mathgroup at smc.vnet.net Sent: Saturday, September 20, 1997 9:28 PM To: mathgroup at smc.vnet.net Subject: [mg8750] [Q] error in Integrate Hi, with Mma 2.2, Integrate[Integrate[ Sqrt[x-y]^2,{x,0,1}],{y,0,1}] gives 0, which is obviously wrong. Am i missing something ? Is there a package or something else i could load to correct this result = ? (theoretical result is 1/3) Thanks in advance. Denis