Subject: FW: [ maxima-Bugs-1051437 ] Trig integral error
From: Billinghurst, David (CALCRTS)
Date: Thu, 21 Oct 2004 23:04:22 +1000
This bug is annoying me enough to want to try and fix it.
Any thoughts on where to start looking?
Bugs item #1051437, was opened at 2004-10-21 22:21
Message generated for change (Comment added) made by billingd
You can respond by visiting:
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1051437&group_id=4933
Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Submitted By: David Billinghurst (billingd)
Assigned to: Nobody/Anonymous (nobody)
Summary: Trig integral error
Initial Comment:
The integral of
2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x));
is wrong for maxima-5.9.1
(%i1) display2d:false;
(%o1) FALSE
(%i2) h: 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x));
(%o2) 2*COT(x)^2*COS(2*x)/(CSC(2*x)+COT(2*x))
(%i3) ih:integrate(h,x);
(%o3) (2*LOG(SIN(x)^2+COS(x)^2+2*COS(x)+1)
+2*LOG(SIN(x)^2+COS(x)^2-2*COS(x)+1)
+COS(2*x))
/2
(%i4) ev(ih,x=1.0,numer)-ev(ih,x=0.5,numer);
(%o4) .6469013090248041
(%i5) quad_qags(h,x,0.5,1);
(%o5) [.1686767378171631,3.37999776996994E-
15,21,0]
(%i6) h2:trigsimp(trigexpand(h));
(%o6) (4*COS(x)^3-2*COS(x))/SIN(x)
(%i7) ih2:integrate(h2,x);
(%o7) LOG(COS(x)+1)+LOG(COS(x)-1)+2*COS(x)^2
(%i8) ev(ih2,x=1.0,numer)-ev(ih2,x=0.5,numer);
(%o8) .1686767378171636
The integral over 0.5 < x < 1.0 at %o4 differs from the
numerical integral %o5 and the analytic integral of an
equivalent expression %o8.
Once this is fixed, activate equation (22) in
share/contrib/diffequations/tests/rtestode_murphy1.mac
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