MathGroup Archive 2007

[Date Index] [Thread Index] [Author Index]

Search the Archive

Integrals involving square roots


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!




  • Prev by Date: Re: Sort with -Infinity fails
  • Next by Date: Regression
  • Previous by thread: Re: Unexpected message 2
  • Next by thread: Re: Integrals involving square roots