Re: integral

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Re: integral

I notice that the TI-89 correctly calculates the derivative of e^(x^2-2x) as (2x-2)*e^(x^2-2x), but when asked for the antiderivative of this result the calculator merely splits it into two terms, each expressing a non-elementary antiderivative:  2S(x*e^(x^2-2x),x) -2S(e^(x^2-2x),x). This distributive strategy, which is apparently the heuristic built into the AOS to handle this sort of situation, fails here.

Thanks to the original poster for observing this -- always nice to have a few examples handy of why the human operator has to be the boss when running power tools. It is going to be possible to "trick" any given rule-driven set of instructions, though naturally systems in common use are going to get smarter and smarter over time. I think adding in a back-tracking routine is needed here. Given the clue this example provides, no doubt it would be possible to come up with a whole range of situations where the only way to get the calculator to perform would be for the user to first make a strategic substitution.

Here's a related question: can we make the TI-89 perform this substitution and come up with the desired result "in front of our eyes"? Entering (2x-2)*e^(x^2-2x)|x^2-2x=u yields (2x-2)*e^u, and what command could we then enter to obtain the desired antiderivative?

        RWW Taylor
        National Technical Institute for the Deaf
        Rochester Institute of Technology
        Rochester NY 14623

        >>>> The plural of mongoose begins with p. <<<<

Brian Hinkle wrote:

Maybe because it takes human intelligence and creativity to do u-subsitution.  Ask the programmers - it might be that the processer simply isn't powerful enough to do something like that. Brian Hinkle
----- Original Message -----
From: Roland Antaki
To: CALC-TI@LISTS.PPP.TI.COM
Sent: Saturday, January 27, 2001 11:44 AM
Subject: integral
 Hello,My name is Carl Antaki.I would like to know why thi TI-89 AMS 2.05 HW-2 don't giveme the integral of  (x-1)*e^(x^2-2x).Is it because the C.A.S is feeble or what?The solution is really simple:(1/2)*e^(x^2-2x).Thank you a lot in advance.