Wrong integration of abs(sin(x)*cos(x))

[pdenapo]

Sage ignores the absolute value in the following symbolic integration.

sage: g=abs(sin(x)*cos(x))
sage: g.integrate(0,2*pi)
0

(the right result is 2, the integrand is positive in the interval so the
integral can never be 0!

sage: version()
'SageMath version 7.6, Release Date: 2017-03-25'

Component: symbolics

Keywords: symbolic integration, absolute value, abs_integrate

Issue created by migration from https://trac.sagemath.org/ticket/23271

[pdenapo]

Description changed:

--- 
+++ 
@@ -1,12 +1,16 @@
 Sage ignores the absolute value in the following symbolic integration.
 
+
+```
 sage: g=abs(sin(x)*cos(x))
 sage: g.integrate(0,2*pi)
 0
+```
 
 (the right result is 2, the integrand is positive in the interval so the
 integral can never be 0! 
 
+```
 sage: version()
 'SageMath version 7.6, Release Date: 2017-03-25'
-
+```

[mforets]

comment:2

from v.8.0 those abs-integrands can be handled with the Giac interface:

sage: g.integrate(0,2*pi, algorithm='giac')
2

besides, there are several related tickets in the symbolic wiki -- integration. there is a link to one Maxima's upstream report in #17511 (should we submit a new upstream report for this one? since they seem to be so related).

[rwst]

comment:3

Replying to @mforets:

(should we submit a new upstream report for this one? since they seem to be so related).

Don't think so.

[fchapoton]

Changed keywords from symbolic integration, absolute value to symbolic integration, absolute value, abs_integrate

[fchapoton]

comment:5

fixed by #27958, that needs review

[fchapoton]

comment:6

already doctested in #27958