Strange Integration "bug" - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html) +--- Forum: HP Prime (/forum-5.html) +--- Thread: Strange Integration "bug" (/thread-12937.html) |
Strange Integration "bug" - chazzs - 05-07-2019 01:42 AM I haven't been here for quite some time, so I'm not sure if this has been mentioned. I just update Software Version 2018 01 24 (13333). If you integrate from -1 to 0.75 the function: sqrt(1-x^2)*(x+2) all is good (2.818). Leave of the multiplication: sqrt(1-x^2)(x+2) all sorts of Warning, constant function scrolling a million miles an hour. Is this typical in CAS? C RE: Strange Integration "bug" - Wes Loewer - 05-07-2019 06:30 PM The Prime CAS has some very powerful features which sometimes produces results that might be different from what you expected, but usually for good reasons. In this case, the sqrt(1-x^2)(x+2) does not mean what you probably think it means. For instance, start with: f(x):=x^2+1 g(x):=x^3 The following is a valid syntax used in textbooks, but not usually allowed on calculators but supported on the Prime: (f*g)(2) --> 40 (f+g)(x+1) --> (x+1)^3+(x+1)^2+1 Notice how the adjacent parentheses do not mean implied multiplication here. They mean "apply the function f+g to x+1". If you use your expression sqrt(1-x^2)(x+2) without the integral, you get: sqrt(1-x^2)(x+2) --> √(1-(x+2)^2) which is correct if you interpret the sqrt(1-x^2) as a function which is using (x+2) as the argument. In general I tell my students to avoid using implied multiplication on any CAS except for the simplest of cases, like 2x+5y=6. The Nspire CAS also has cases that confuse my students, like x(x+1) being rejected since it could be implied multiplication or it could be a function named x. The inspire allows y(x+1) or x(y+1) as functions. As humans, we would likely interpret y(x+1) as a function, but we might interpret x(y+1) as implied multiplication. Understanding human thought is tricky business. :-) Even simple things like 1/2pi has different meaning on different calculators, even different models from the same brand. |