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Re: Integrals involving square roots

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[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 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[1] and evaluate it, Mathematica complains that the integral "is 
incomplete; more input is needed."


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