Strange Integration "bug"
05-07-2019, 01:42 AM
Post: #1
 chazzs Junior Member Posts: 22 Joined: Feb 2015
Strange Integration "bug"
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
05-07-2019, 06:30 PM
Post: #2
 Wes Loewer Member Posts: 162 Joined: Jan 2014
RE: Strange Integration "bug"
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.
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.
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