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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: <es90ol$2lt$1@smc.vnet.net>

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[1]:=
> \!\(\[Integral]\_\(-3\)\%3\(\[Integral]\_\(-\@\(9 - x\^2\)\)\%\(\@\(9 -
> \x\^2\)\)\(\[Integral]\_0\%\(y - 3\)2 y \[DifferentialD]z \[DifferentialD=
]y
> \[DifferentialD]x\)\)\)
> Out[1]=
> \!\(\(81\ \[Pi]\)\/2\)
> In[5]:=
> \!\(\[Integral]\_0\%2\(\[Integral]\_\(-R\)\%R\( Rz\^2\/\@\(R\^2 - x\^2\)\)
> \\[DifferentialD]x \[DifferentialD]z\)\)
> Out[5]=
> \!\(\(-2\)\ \[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!