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 >