#8624: integral of abs(cos(x))*sin(x) gives false results
----------------------+-----------------------------------------------------
Reporter: jeroen | Owner: burcin
Type: defect | Status: closed
Priority: minor | Milestone: sage-4.6.1
Component: calculus | Resolution: fixed
Keywords: | Author: Jason Grout
Upstream: N/A | Reviewer: Burcin Erocal
Merged: | Work_issues:
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Changes (by mvngu):
* status: needs_work => closed
* resolution: => fixed
Comment:
This is fixed at ticket #10187 by upgrading Maxima to version 5.22.1:
{{{
[mv...@sage sage-4.6.1.alpha3]$ ./sage
----------------------------------------------------------------------
| Sage Version 4.6.1.alpha3, Release Date: 2010-12-05 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
**********************************************************************
* *
* Warning: this is a prerelease version, and it may be unstable. *
* *
**********************************************************************
sage: integral(abs(cos(x))*sin(x),(x,pi/2,pi))
1/2
sage: numerical_integral(abs(cos(x))*sin(x),pi/2,pi)
(0.49999999999999994, 5.5511151231257819e-15)
sage: integrate(sqrt(cos(x)^2+sin(x)^2), x,0,2*pi)
2*pi
}}}
Mathematica 6.0 also agrees:
{{{
Mathematica 6.0 for Linux x86 (64-bit)
Copyright 1988-2007 Wolfram Research, Inc.
In[1]:= Integrate[Abs[Cos[x]] * Sin[x], {x,Pi/2,Pi}]
1
Out[1]= -
2
In[2]:= Integrate[Sqrt[Cos[x]^2 + Sin[x]^2], {x,0,2*Pi}]
Out[2]= 2 Pi
}}}
So I'm closing this ticket as fixed.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8624#comment:13>
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