Re: 50g integration oddity Message #15 Posted by Karl Schneider on 13 May 2009, 3:23 p.m., in response to message #1 by dbatiz
"dbatiz" 
The oddity is rooted in the CAS for the predecessors of the HP50g. On the 1990's HP49G, INTVX obtains the following indefinite integral in symbolic form:
'INV(XROOT(3,SQ(X)+6*X+9))'
INTVX
(3*sqrt(cbrt(X^2+6X+9)))
The negative sign out front negates the correct answer.
Interestingly, even though the HP49G did not reduce the perfect square in the integrand, it made a difference: Change the +9 to +10 or +8, and the HP49G fails to find a symbolic solution. However, the leading minus sign is still present in the result, which is a an evaluable command for numerical integration.
There are indeed multiple mathematical answers for cube root and square root. However, if principal and/or realvalued roots are always to be taken, I submit that HP's CAS answer is incorrect.
The correct symbolic integral is
3*cbrt(X+3)
Certainly, there is only one correct definiteintegral answer, which all of the models with builtin integration will find using numerical methods.
The moral: Know your calculus, so that you will always recognize balderdash in problems such as these.
(Edited to add some content.)
 KS
Edited: 14 May 2009, 1:47 a.m. after one or more responses were posted
