[Maxima-bugs] [ maxima-Bugs-2761756 ] possible integration bug

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

Bugs item #2761756, was opened at 2009-04-14 07:56
Message generated for change (Comment added) made by rtoy
You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2761756&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: None
Group: None
Status: Closed
>Resolution: None
Priority: 5
Private: No
Submitted By: Nobody/Anonymous (nobody)
Assigned to: Nobody/Anonymous (nobody)
Summary: possible integration bug

Initial Comment:
I tried below.

(%i2) declare(n,integer) ;
(%o2) done
(%i3) integrate(sin(n*%pi*x/a)*(sin(%pi*x/a))^3,x,-a,a) ;
(%o3) 0

Now, (sin(sin(%pi*x/a))^3 can be converted to (3*sin(%pi*x/a)-sin(3*%pi*x/a))/4 and if I do above
integration manually, it yields that the result is 0 for any n except 1 or 3.  If n=1 result should be 3/4*a
and if n=3 result should be -a/4 but not zero for both cases.  Is this a bug?

Maxima version: 5.17.1
Maxima build date: 20:10 3/10/2009
host type: powerpc-apple-darwin8.11.0
lisp-implementation-type: CMU Common Lisp
lisp-implementation-version: Stage 3 20071108T014921 (19D)


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

>Comment By: Raymond Toy (rtoy)
Date: 2009-08-19 21:22

Message:
Reopening bug.

Shouldn't maxima at least ask if n = 1 or something?  When n = 1, the
integrand is sin(%pi*x/a)^4, so the integral can't be zero.

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

Comment By: Dieter Kaiser (crategus)
Date: 2009-08-19 18:53

Message:
When n is not declared to be an integer the answer is:

(%i6) integrate(sin(n*%pi*x/a)*(sin(%pi*x/a))^3,x,-a,a);
(%o6) 12*a*sin(%pi*n)/(%pi*n^4-10*%pi*n^2+9*%pi)

This answer simplifies correctly to zero when n is an integer.

Closing this bug report as invalid.

Dieter Kaiser

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

Comment By: Nobody/Anonymous (nobody)
Date: 2009-04-14 10:02

Message:
Ok, it seems it an orthogonal problem.  
(%i7) integrate(sin(n*%pi*x)*sin(%pi*x),x,-1,1) ;
(%o7) 0


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

You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2761756&group_id=4933