In Maxima 5.24.0:
(%i11) integrate(x*signum(x^2-1/4),x,-1,0);
1
(%o11) -
2
But the picture makes it pretty clear this should be -1/4.
Is this antideriv ok?
(%i15) integrate(x*signum(x^2-1/4),x);
! 2 1!
!x - -!
! 4!
(%o15) --------
2
This was originally reported at the Sage trac at http://trac.sagemath.org/sage_trac/ticket/11590
Barton Willis
2011-07-30
By the way:
(%i4) load(abs_integrate)$
Correct antiderivative:
(%i5) 'integrate(x*signum(x^2-1/4),x);
(%o5) abs(x^2-1/4)/2
Correct definite integral
(%i6) 'integrate(x*signum(x^2-1/4),x,-1,0);
(%o6) -1/4
Anonymous
2011-08-24
Good point, and we're working on getting that loaded in automatically. Doesn't fix the original problem, though.
Anonymous
2012-02-01
Update: why doesn't regular integrate work? Only 'integrate does.
(%i5) display2d:false;
(%o5) false
(%i6) integrate(x*signum(x^2-1/4),x,-1,0);
(%o6) 1/2
(%i7) 'integrate(x*signum(x^2-1/4),x,-1,0);
(%o7) -1/4
Again, this doesn't fix the problem that the answer is just wrong currently :( but at least would help use get it to work right in Sage.