Special delimited oscillators that maxima can't solve it.
Subject: Special delimited oscillators that maxima can't solve it.
From: J.C. Pizarro
Date: Fri, 18 Apr 2008 04:08:18 +0200
On 2008/4/18, J.C. Pizarro <jcpiza at gmail.com>, i wrote:
> On 2008/4/16, Richard Fateman <fateman at cs.berkeley.edu> wrote:
> > I haven't followed all of this, but by a change of variables,
> > integrate(cos(1/x),x,0,2/%pi)
> > is integrate(cos(t)/t^2,t, %pi/2, inf);
> ...
>
> You did a mistake, your change of variables t=1/x doesn't match symbolically
> your integrals. I can't presume anything "mathematically" with human
> suppositions because otherwise it can be incorrect simplification.
>
> integrate(cos(1/x),x,0,2/%pi) is NOT integrate(cos(t)/t^2,t, %pi/2, inf);
> ...
> So, you mistaked your matching by the sign symbol '-'.
>
> integrate(cos(1/x),x,0,2/%pi) = - integrate(cos(t)/(t^2),t,%pi/2, inf)
I'm sorry, i mistaked in the up and down limits of the definite integral
integrate(cos(1/x),x,0,2/%pi) = - integrate(cos(t)/(t^2),t,inf,%pi/2)
It's true that integrate(f(x),x,a,b) = - integrate(f(x),x,b,a) , so that
integrate(cos(1/x),x,0,2/%pi) = integrate(cos(t)/(t^2),t,%pi/2,inf)
as said above Richard Fateman. I'm sorry much, thanks Richard Fateman.
> I'm near to solve it using the simplification by the substitution method
> trying to integrate cos(x)/(x^2) dx later due to
>
> integrate(cos(1/x),x,0,2/%pi) = - integrate(cos(t)/(t^2),t,%pi/2, inf)
>
I'm near to solve it using the simplification by the substitution method
trying to integrate cos(x)/(x^2) dx later due to
integrate(cos(1/x),x,0,2/%pi) = integrate(cos(t)/(t^2),t,%pi/2, inf)
Sincerely, J.C.Pizarro