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[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." Regards, Jean-Marc