## #1692 romberg(sin(x)^3,x,0,2*%pi) does't work

closed
nobody
5
2009-06-27
2009-06-12
Anonymous
No

Good day!
I have problem with my Maxima:
build_info()\$
Maxima version: 5.16.2
Maxima build date: 7:44 8/18/2008
host type: i686-pc-mingw32
lisp-implementation-type: GNU Common Lisp (GCL)
lisp-implementation-version: GCL 2.6.8

When I integrate romberg(sin(x)^3,x,0,2*%pi) I get error:

`romberg' failed to converge
-- an error. To debug this try debugmode(true);

And if power is 5,7 and so on.

What's wrong?

## Discussion

• Dieter Kaiser - 2009-06-12
• status: open --> pending

• Dieter Kaiser - 2009-06-12

There have been related reports in the past. romberg tries to find a numerical solution, but is not always succesful. There are better routines like the quadpack functions to do a numerical integration. There is nothing wrong with the implementation. It is a weakness of the romberg algorithm.

Maxima can calculate an exact definite integral for the function of this bug report and the more general function sin(x)^n, with n a positive integer. The results are:

(%i1) declare(n,odd)\$
(%i2) assume(n>0)\$
(%i3) integrate(sin(x)^n,x,0,2*%pi);
(%o3) 0

(%i4) declare(k,even)\$
(%i5) assume(k>0)\$
(%i6) integrate(sin(x)^k,x,0,2*%pi);
(%o6) 2*beta(1/2,(k+1)/2)

Setting this bug report to "won't fix" and the status to pending.

Dieter Kaiser

• Robert Dodier - 2009-06-12

Well, the problem with this integral is that it is exactly zero, which makes it difficult for any numerical method. (quad_qags returns approx 1e-17 and prints a warning message.)

Agreed that we won't try to fix it, but it's not just a weakness in romberg.

• SourceForge Robot - 2009-06-27
• status: pending --> closed

• SourceForge Robot - 2009-06-27

This Tracker item was closed automatically by the system. It was
previously set to a Pending status, and the original submitter
did not respond within 14 days (the time period specified by