Error when integrating absolute value

[parisse]

(12-08-2019 11:35 PM)pinkman Wrote:  

(12-06-2019 08:42 PM)parisse Wrote:  Please read the whole warning. The problem comes from singulatiries in sign(cos(variable_name)) inside the antiderivative.

Hi Bernard, thanks for trying to help us, but I’m really confused or puzzled by your answer that I don’t understand.
I know the problem of the singularities, but for me there is no doubt that ∫(ABS(cos(x)),x,-π/2,3*π/2) = 4, and ∫(k*ABS(cos(x)),x,-π/2,3*π/2) = k*4 in the real domain, k being a constant.

Am I wrong?

No, but ask yourself, how did you get this result? You probably cut the integral in several parts. The problem here is to find the cut positions. You have to solve an equation for that, and after I had problems with more complicated inputs, I decided to solve this equation only if it was univariate. This is not the case if there is a parameter, that's why you got the warning and a wrong answer. I have already modified the source code to solve it for this input because the dependancy in k can easily be removed, now you will get 4*k. But keep in mind that in other situations, it might be wrong, you should always read carefully the warnings and check your answer if there is a warning.