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MathGroup Archive 2000

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Re: step fn of sin

  • To: mathgroup at smc.vnet.net
  • Subject: [mg21596] Re: step fn of sin
  • From: "Kevin J. McCann" <kevinmccann at home.com>
  • Date: Sun, 16 Jan 2000 22:43:45 -0500 (EST)
  • References: <85s1ek$ajh@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Interesting.  A plot of the following gives the result that I think you
want.  Not really antisymmetric, but I understand what you meant.

Delta = 0.001;
G[y_ ] :=
 Sign[y]* Delta*Plus @@ Table[
     theta[Sin[x]],
     {x, 0, y, Sign[y]*Delta}]
G[0]=0;

What is interesting is Mathematica's result.  Your F[-5] gives zero, but a plot of
the integrand shows that it should be (pi-5).  I am surprised that Mathematica 
doesn't just regurgitate the integral, since there is no easy analytic
solution to the integral.  If I had the initiative, I could probably kluge
up an answer with Mod's, etc., but ...

Kevin

"Naum Phleger" <naum at cava.physics.ucsb.edu> wrote in message
news:85s1ek$ajh at smc.vnet.net...
>     I was working with integrals of theta functions of other functions and
> found something didn't do what I wanted it to.  I would love any help
> explaining my output.  Here is basically what I am doing.  First I define
my
> step fn.  Then I try to integrate it of a sin fn.  like this.
>
>     theta[x_]= If [ x<0 , 0 , 1 ]
>
>     F[y_]=Integrate [ theta[ Sin[x] ],{ x , 0 , y } ]
>
>     Plot[ F[y] , { x , -4 pi , 4 pi }
>
> This gives what you would expect for x>0 , it gets bigger in sections with
> const. slope alternating by flat sections with the average height about
x/2.
>
> try it and see the x<0 , it doesn't make any sense to be.  I think this
> should be an anti-symmetric function but it isn't.  Thanks for any help.
>
>         -NAUM
>



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