Numerical integration with maxima

[Claude]

Dear readers

I would like to numerically integrate the function abs(sin(x)) over the
domain 0 to 2*pi.

I've defined the function
f=abs(sin(x))

and then I called

integrate(f, x, 0, 2*pi)

But now I don't know how to numerically evaluate this integral.

Manually, it is easy to see that the result should be 4, but how to ask
maxima to compute this ?

Similarly, I cannot plot this function over the same domain. I've tried :

wxplot2d([abs(sin(x))], [x,0,6.28])$

which gives the expected graph, but, if I replace the value 6.28 by 2*pi,
wxmaxima says that

plotting: range must be of the form [variable, min, max]; found: [x,0,2*pi]


Can you please give me some advice?

Thank you in advance for your help

[Nasser M. Abbasi]

fyi;

If you do not get answer here (I myself do not use Maxima) you
can try the Maxima mailing list

http://maxima.sourceforge.net/maximalist.html

[James Cloos]

>>>>> "C" == Claude <cla...@nospam.invalid> writes:

Just a couple of notes:

C> I've defined the function
C> f=abs(sin(x))

Use either:

f:abs(sin(x));

or:

f(x):=abs(sin(x));

C> integrate(f, x, 0, 2*pi)

Use 2*%pi.

C> But now I don't know how to numerically evaluate this integral.

More importantly, integrate() is for symbolic integration. For
numerical integration use quad_qag() and the related functions.

Try:

quad_qag(abs(sin(x)), x, 0, 2*%pi, 2);

for a 2nd order approximation. I get the result:

[4.0, 4.440892098500626e-14, 63, 0]

the values in the list are theapproximation, the approx error, the
number of evaluations and an error code. 0 means no error. So the
result is 4.0 +- 4.440892098500626e-14.

Try:

? quad_qag

and:

?? QUADPACK

in maxima.

Or read the QUADPACK sections of the info or printable manual.

-JimC
--
James Cloos <cl...@jhcloos.com> OpenPGP: 1024D/ED7DAEA6

[Richard Fateman]

On 11/6/12 2:46 AM, Claude wrote:
> Dear readers
>
> I would like to numerically integrate the function abs(sin(x)) over the
> domain 0 to 2*pi.

use %pi

[Claude]

Thank you all for your help !

claude