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[Maxima-bugs] [ maxima-Bugs-2142758 ] integrate(sqrt(2-2*x^2)*(sqrt(2)*x^2+sqrt(2))/(4-4*x^2), x, 0,
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From: SourceForge.net <no...@so...> - 2008-10-08 15:05:59
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Bugs item #2142758, was opened at 2008-10-02 13:01 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2142758&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: Lisp Core - Integration Group: None >Status: Closed >Resolution: Fixed Priority: 5 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(sqrt(2-2*x^2)*(sqrt(2)*x^2+sqrt(2))/(4-4*x^2),x,0, Initial Comment: I'm using Maxima 5.16.3 integrate(sqrt(2-2*x^2)*(sqrt(2)*x^2+sqrt(2))/(4-4*x^2),x,0,1); evaluates to -3*%pi/4, which is wrong (should be positive and equal to 3*%pi/8). If one simplifies this expression to integrate(sqrt(1-x^2)*(x^2+1)/(2-2*x^2),x,0,1); it evaluates still to -3*%pi/4. But this: integrate(sqrt(1-x^2)*(x^2+1)/(1-x^2),x,0,1); evaluates correctly to 3*%pi/4 Hope this helps you to improve this really great program! My best regards to all who contribute. Ivo e-mail: ivo dot bloechliger at kanti dash wohlen dot ch ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2008-10-08 11:05 Message: Fixed in irinte.lisp, rev 1.23. ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2008-10-08 10:51 Message: The problem is caused by the routine pns-intir3 in irinte.lisp. A typo in the derivation (and implementation) caused the integrand to be multiplied by an extra -4. After fixing this, maxima now returns 3*%pi/8. ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2008-10-06 11:52 Message: FWIW, maxima computes all of these definite integrals by computing the antiderivative and substituting the limits. For all but the last integral, the antiderivative has the wrong sign. I do not know why the sign is wrong. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2142758&group_id=4933 |