Some integrals with problematic evaluation

[quinyu]

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.

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."

Of course, unlike with PCs, the hardware in the calculators varies much more wildly, so actual comparison of what the raw iron could do are close to impossible, never mind what the programs on it are able to do. Using FLOPS or something similar is close to being irrelevant here, I feel. And while it's certainly nice for the calculator users to get a result quickly, my personal feeling is that it's more important for the users to be able to trust their calculators that if/when it gives an answer, it's actually a correct answer. Let them be aware that the system has its limits - but let them know when the question they asked of the system can be answered (correctly, mind you) by the same system, and that they are getting that result.

Before assuming that I'm praising it to high heavens, there was a case on the CPII where I needed to switch to Complex mode to evaluate an integral, even though there was nothing related to complex numbers either in the integrated function or the corresponding result. My emotion at that time was that it was underhanded. How are you supposed to deduce by looking at an integral that the calculator will only be able to handle it properly in complex mode, when it has only perfectly real functions and terms in it? You can't. So this is where I feel tricked, cheated, call it what you will... but I'll cut this rant here, it's already longer than I originally intended it to be.