Integrals involving square roots

*To*: mathgroup at smc.vnet.net*Subject*: [mg73854] Integrals involving square roots*From*: "Andre Giroux" <giroux at dms.umontreal.ca>*Date*: Fri, 2 Mar 2007 06:27:45 -0500 (EST)

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!