[Maxima-bugs] [ maxima-Bugs-2989983 ] wrong integration answer

[SourceForge.net <no...@so...>]

Bugs item #2989983, was opened at 2010-04-20 19:35
Message generated for change (Comment added) made by alex108
You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989983&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: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Nobody/Anonymous (nobody)
Assigned to: Nobody/Anonymous (nobody)
Summary: wrong integration answer

Initial Comment:
When using sage, and thus Maxima, for the integration of:

Cos(T + w) / (1+e cos(T)^2 from 0 to 2*pi, sage (and thus maxima?) gives 0 as answer.
There maple gives the answer: -2*pi*e*cos(w)/1-e^2)^1.5

the correct commands in sage 4.3.5 are (don't know them in maxima):
sage: e = var('e')
sage: w = var('w')
sage: T = var('T')
sage: assume(1-e^2>0)
sage: integrate(cos(w+T)/(1+e*cos(T))^2, T, 0, 2*pi)
0

----------------------------------------------------------------------

Comment By: Aleksas Domarkas (alex108)
Date: 2010-04-21 00:57

Message:
Solving with maxima 5.21.0 :

(%i1) S: 'integrate(cos(T+w)/(1+e*cos(T))^2, T, 0, 2*%pi)$
(%i2) first(%)$
(%i3) expand(%)$
(%i4) f:trigexpand(%)$
(%i5) F:integrate(f,T)$
"Is  "e^2-1.0"  positive or negative?"negative;
 Antiderivative F is discontinous at T=%pi. For example
(%i6) wxplot2d([F], [T,0,2*%pi]),e=1/2,w=1$
plot2d: expression evaluates to non-numeric value somewhere in plotting
range.
(%t6)  << Graphics >>
 Then integral is equal
(%i7) limit(F,T,%pi,minus)-ev(F,T=0)+ev(F,T=2*%pi)-limit(F,T,%pi,plus)$
(%i8) sol:ratsimp(%);
(%o8) -(2*%pi*e*sqrt(1-e^2)*cos(w))/(e^4-2*e^2+1)
 This is same as Maple answer:
(%i9) -2*pi*e*cos(w)/(1-e^2)^1.5$ 

----------------------------------------------------------------------

You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2989983&group_id=4933