BTW :
```
sage: a, b = var("a, b")
sage: f(x) = floor(x)^2
sage: F(x) = f(x).integrate(x) ; F
x |--> x*floor(x)^2
sage: def G(x): return numerical_integral(f, 0, x)[0]
sage: plot([F, G], (0, 3))
Launched png viewer for Graphics object consisting of 2 graphics primitives
```
[image: tmp_7n_jxgco.png]
Giac's "antiderivative" implicitly adds `heaviside(x-u)^2` terms... Again,
this is wrong...
Le vendredi 3 février 2023 à 10:31:17 UTC+1, Emmanuel Charpentier a écrit :
> BTW :
>
> ```
> sage: a, b = var("a, b")
> sage: f(x) = floor(x)^2
> sage: f(x).integrate(x, a, b)
> // Giac share root-directory:/usr/local/sage-9/local/share/giac/
> // Giac share root-directory:/usr/local/sage-9/local/share/giac/
> Added 0 synonyms
> No checks were made for singular points of antiderivative
> floor(sageVARa)^2*sageVARx for definite integration in [sageVARa,sageVARb]
> -a*floor(a)^2 + b*floor(a)^2
> ```
>
> Even accepting `x*floor(x)^2` as an antiderivative of `floor(x)`, this
> *definite* integral is wrong, *wrong*, **wrong**. One could expect :
>
> ```
> sage: F(x) = f(x).integrate(x) ; F
> x |--> x*floor(x)^2
> sage: F(b) - F(a)
> -a*floor(a)^2 + b*floor(b)^2
> ```
>
> Something is amiss in Giac's definite integration. Is thois already known ?
>
>
> Le vendredi 20 janvier 2023 à 18:17:52 UTC+1, Georgi Guninski a écrit :
>
>> I have theoretical reasons to doubt the correctness
>> of integrals involving `floor`.
>>
>> The smallest testcases:
>>
>> sage: integrate(floor(x)^2,x)
>> // Giac share root-directory:/usr/share/giac/
>> // Giac share root-directory:/usr/share/giac/
>> Added 0 synonyms
>> x*floor(x)^2
>>
>> sage: integrate(2**floor(x),x)
>> 2^floor(x)*x
>>
>> Would someone check with another CAS or prove/disprove by hand?
>>
>
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