integral of abs(cos(x))*sin(x) gives false results

[jdemeyer]

The integral of abs(cos(x))*sin(x) returns the result as if abs() is ignored:

sage: integral(abs(cos(x))*sin(x),(x,pi/2,pi))
-1/2

while

sage: numerical_integral(abs(cos(x))*sin(x),pi/2,pi)
(0.49999999999999994, 5.5511151231257819e-15)

CC: @kcrisman

Component: calculus

Author: Jason Grout

Reviewer: Burcin Erocal

Issue created by migration from https://trac.sagemath.org/ticket/8624

[jasongrout]

comment:1

This might be related to this bug, which should be somewhere on trac:

sage: integrate(sqrt(cos(x)^2+sin(x)^2), x,0,2*pi)       
pi

[jasongrout]

comment:2

#8729 may point to a solution

[jasongrout]

comment:4

This patch fixes the problem, but introduces some other doctest errors that should be fixed.

[jasongrout]

Author: Jason Grout

[kcrisman]

comment:5

Make sure it doesn't introduce any errors - sometimes loading extra Maxima packages causes trouble. Also note that elsewhere there are complaints about Maxima start time, which this would contribute to.