Some integrals with problematic evaluation

[parisse]

(04-02-2016 08:04 PM)quinyu Wrote:  Sure, we fully agree on this one. The question is, so to say, when does the user start to "see the break," that is, realise when he should do that switch. The term "complicated" in itself is a very subjective term. And then - most users, when they see that the calculator/CAS does return a result that isn't a symbolic explosion and on first glance looks plausible, they prefer to assume that the result is correct. You, or me for that matter, know better, but the "average" user doesn't, which can lead to a number of unfortunate consequences.

It should be the job of math teachers to explain to students when they can trust a calculator, and when they should not. Unfortunately many math teachers do not want to learn that (they say it is not math ... a good excuse not to learn).

Quote:When the calculator says (in one form or the other) "cannot do," they surely make a switch, but not otherwise, since in their judgement the handheld/calculator is still capable of returning a (what they think) correct answer. Extreme long waiting times might influence this judgement of course, suggesting it might be better to switch over to some other system, with a better hardware foundation. In one manner, I respect the Classpad II for this, for it dares to return the original integral as an answer, indicating "sorry, man, this is above my level."

This could only be done by being very conservative. In other words by adding more and more checks, you ease use for students who do not want to learn a bit of maths, but in the same time you will add limits for students who are accepting to learn a bit of maths. My opinion is that it is not the right way to go.