On 11/23/2011 04:07 PM, Michel Talon wrote:
> integrate(1/sqrt(2-2*cos(x)),x,-%pi/2,%pi/2)
> I have just tried it on maxima-5.25.1 and it gives:
> Principal Value
> (%o3) 0
> This is one more problematic result compared to Fateman's list!
> We have the indication that a principal value occurs somewhere. In fact
> in the middle of the integration range we have a problem at x=0 where
> 2-2*cos(x) ~ x^2 and thus we have 1/sqrt(1/x^2) ~ 1/x
Hi,
if you try integrate(1/sqrt(x^2),x,-%pi/2,%pi/2), which has a similar
problem,
you get the answer 'integrate(1/abs(x),x,-%pi/2,%pi/2) which is a divergent
integral. I think 1/sqrt(x^2) and 1/sqrt(2-2*cos(x)) should be treated
in the
same way.
In the applications I'm used to, whenever I run across sqrt() I am
dealing with a distance, which should be positive, so:
1/sqrt(2-2*cos(x)) ~ 1/|x| and not 1/x or -1/x or -1/|x|. In other
cases, since
we are talking about a discontinuous function, one should specify which
of the 4 functions we are referring to. Perhaps Maxima should ask for the
sign of 1/sqrt(2-2*cos(x)) for positive and negative x?
Regards,
Jaime