Opened 3 years ago
Closed 5 months ago
#24117 closed defect (fixed)
integrate(sqrt(14*sin(x)^2),x) is wrong
Reported by:  slabbe  Owned by:  

Priority:  major  Milestone:  sage9.2 
Component:  calculus  Keywords:  maxima, abs_integrate 
Cc:  kcrisman, jhpalmieri, slelievre  Merged in:  
Authors:  Frédéric Chapoton  Reviewers:  Sébastien Labbé 
Report Upstream:  N/A  Work issues:  
Branch:  9406e0a (Commits)  Commit:  9406e0adb95727f9036cc7dd0c58f999100bdd04 
Dependencies:  Stopgaps: 
Description
I received an email from Pierre Arnoux saying that this is wrong:
sage: integrate (sqrt(14*sin(x)^2),x, algorithm='maxima') 1/12*sin(3*x) + 1/4*sin(x)
Quoting what Pierre says: "Ce qui est visiblement faux: il y a un point d'inflexion horizontal en 0 alors que la fonction à intégrer vaut 1 en 0, ça ne peut pas être une primitive. Estce que vous avez une idée de ce qui ne marche pas?"
Other programs in Sage just can't solve this integral:
sage: integrate (sqrt(14*sin(x)^2),x, algorithm='fricas') # installed with "sage i fricas" integral(sqrt(4*cos(x)^2  3), x) sage: integrate (sqrt(14*sin(x)^2),x, algorithm='giac') integrate(sqrt(4*sin(x)^2 + 1), x) sage: integrate (sqrt(14*sin(x)^2),x, algorithm='sympy') ....does not halt...
Change History (11)
comment:1 Changed 3 years ago by
comment:2 Changed 3 years ago by
Here is how I would describe this bug in the integrate function. (This can be turned into a doctest when this bug is resolved.)
sage: f(x) = sqrt(14*sin(x)^2) sage: F(x) = integrate(f(x), x) sage: F(x) 1/12*sin(3*x) + 1/4*sin(x)
Comparing the derivative of F with f shows this is wrong.
sage: g(x) = diff(F(x), x) sage: g(x) 1/4*cos(3*x) + 1/4*cos(x) sage: f(0), g(0) (1, 0)
Looking at the plots of f and F also reveals an error:
sage: xr = (0.4, 0.4) sage: plot(f, xr, color='blue') + plot(F, xr, color='red')
Here, f (blue curve) is 1 at 0, so its primitive F (red curve) should have slope 1 at 0, instead of 0.
comment:3 Changed 3 years ago by
There are half a dozen similar tickets to this. The reason is that Sage uses a (now) unmaintained package of Maxima, see #12731 for an overview.
comment:4 Changed 19 months ago by
 Keywords abs_integrate added
comment:5 Changed 18 months ago by
this one is fixed by #27958, that needs review
comment:6 Changed 5 months ago by
 Branch set to u/chapoton/24117
 Cc kcrisman jhpalmieri slelievre added
 Commit set to 020d526ec76410f32c315eb73ef2d4c180d3a35c
 Status changed from new to needs_review
comment:7 Changed 5 months ago by
 Commit changed from 020d526ec76410f32c315eb73ef2d4c180d3a35c to 9406e0adb95727f9036cc7dd0c58f999100bdd04
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
9406e0a  add doctest for 24117

comment:8 Changed 5 months ago by
 Milestone changed from sage8.1 to sage9.2
comment:9 Changed 5 months ago by
 Status changed from needs_review to positive_review
comment:10 Changed 5 months ago by
 Reviewers set to Sébastien Labbé
comment:11 Changed 5 months ago by
 Branch changed from u/chapoton/24117 to 9406e0adb95727f9036cc7dd0c58f999100bdd04
 Resolution set to fixed
 Status changed from positive_review to closed
See also #18821.