|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
The oddity is rooted in the CAS for the predecessors of the HP-50g. On the 1990's HP-49G, INTVX obtains the following indefinite integral in symbolic form:
The negative sign out front negates the correct answer.
Interestingly, even though the HP-49G did not reduce the perfect square in the integrand, it made a difference: Change the +9 to +10 or +8, and the HP-49G 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 real-valued roots are always to be taken, I submit that H-P's CAS answer is incorrect.
The correct symbolic integral is
Certainly, there is only one correct definite-integral answer, which all of the models with built-in 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.)
Edited: 14 May 2009, 1:47 a.m. after one or more responses were posted