       Re: Integrals involving square roots

• To: mathgroup at smc.vnet.net
• Subject: [mg73915] Re: Integrals involving square roots
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Sat, 3 Mar 2007 00:59:21 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <es90ol\$2lt\$1@smc.vnet.net>

```Andre Giroux wrote:
> 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 correctly.
> So beware!
>
>
>

For the first integral, could you, please, post some syntacticly correct
code, preferably in ImputForm? When I copy and past the expression after
In and evaluate it, Mathematica complains that the integral "is
incomplete; more input is needed."

Regards,
Jean-Marc

```

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