integral



On Tue, Apr 08, 2008 at 07:10:53AM -0500, maxima-request at math.utexas.edu wrote:
>
> Dear list,
> 
> I would like to obtain a numerical value for the variation of the
> third function at
> 
> http://en.wikipedia.org/wiki/Bounded_variation#Examples
> 
> namely, the one with x^2*sin(1/x).
> 
> I would like to do this using Maxima.  The integral I need to
> calculate is
> 
> (%i8) integrate(abs(2*x*sin(x)-cos(1/x)), x, 0, 2/%pi);
>                            2
>                           ---
>                           %pi
>                          /
>                          [    !                 1 !
> (%o8)                    I    !2 x sin(x) - cos(-)! dx
>                          ]    !                 x !
>                          /
>                           0

Oops... I now noticed that I've made a typo... this explains why
some people's result deviated quite from what I expected... the
integral should have been:

(%i77) integrate(abs(2*x*sin(1/x)-cos(1/x)), x, 0, 2/%pi);
                           2
                          ---
                          %pi
                         /
                         [    !      1          1 !
(%o77)                   I    !2 sin(-) x - cos(-)! dx
                         ]    !      x          x !
                         /
                          0

In the mean while, using quad_qag, i have a solution which is correct
for about 3 or 4 digits and that satisfies my needs.

However, being enthousiastic about this problem and while learning to
use Maxima, I am now also trying to write a maxima script that
integrates between the roots of this function.  I'm using find_root, but
being quite a maxima newbee, I'm struggling a bit with the syntax... but
anyway... just give me some time and maybe I'll get there :-)

Regards,
Bart

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	"Share what you know.  Learn what you don't."