Incorrect result in simple integral: integrate(sqrt(sin(t)^2+cos(t)^2), t, 0, 2*%pi)
Subject: Incorrect result in simple integral: integrate(sqrt(sin(t)^2+cos(t)^2), t, 0, 2*%pi)
From: Robert Marik
Date: Fri, 16 Oct 2009 20:51:43 +0000 (UTC)
Dear Maxima developers
the following integral is evaluated in Maxima into %pi, but it should be 2*%pi
integrate(sqrt(sin(t)^2+cos(t)^2),t,0,2*%pi)
Do you know about this bug? This bug has been reported on Sage forum
http://groups.google.cz/group/sage-devel/browse_thread/thread/f82e24efdfe23b07
Old Maxima gives correct result.
Maxima 5.13.0 http://maxima.sourceforge.net
Using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (aka GCL)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
This is a development version of Maxima. The function bug_report()
provides bug reporting information.
2 2
(%i1) integrate(sqrt(sin (x) + cos (x)), x, 0, 2 %pi)
(%o1) 2 %pi
The Maxima included in Sage gives %pi. According to kcrisman, the CVS version
has the same problem.
marik at asus-eee:/opt/sage$ ./sage
----------------------------------------------------------------------
| Sage Version 4.1.2, Release Date: 2009-10-14 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: maxima("integrate(sqrt(sin(t)^2+cos(t)^2),t,0,2*%pi)")
%pi
sage:
Yours sincerely
Robert Marik