Re: Integrals involving square roots
- To: mathgroup at smc.vnet.net
- Subject: [mg73911] Re: Integrals involving square roots
- From: "dimitris" <dimmechan at yahoo.com>
- Date: Sat, 3 Mar 2007 00:57:11 -0500 (EST)
- References: <email@example.com>
Sorry folk, I was not able to none of your integrals! Try convert everything into InputForm! Cheers Dimitris =CF/=C7 Andre Giroux =DD=E3=F1=E1=F8=E5: > Hi All. > Mathematica is very unreliable when it computes integrals involving square > roots. The following were obtained running Mathematica 5.2 and 5.1 with > Windows XP pro: > > In:= > \!\(\[Integral]\_\(-3\)\%3\(\[Integral]\_\(-\@\(9 - x\^2\)\)\%\(\@\(9 - > \x\^2\)\)\(\[Integral]\_0\%\(y - 3\)2 y \[DifferentialD]z \[DifferentialD= ]y > \[DifferentialD]x\)\)\) > Out= > \!\(\(81\ \[Pi]\)\/2\) > In:= > \!\(\[Integral]\_0\%2\(\[Integral]\_\(-R\)\%R\( Rz\^2\/\@\(R\^2 - x\^2\)\) > \\[DifferentialD]x \[DifferentialD]z\)\) > Out= > \!\(\(-2\)\ \[Pi]\ Rz\^2\) > > In both cases, the sign is wrong and, with the first integral, it is not > obvious. Interestingly, Mathematica 5.0 computes these integrals correctl= y=2E > So beware!