Re: step fn of sin

*To*: mathgroup at smc.vnet.net*Subject*: [mg21605] Re: [mg21591] step fn of sin*From*: BobHanlon at aol.com*Date*: Sun, 16 Jan 2000 22:43:51 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Clear[x, y, F, theta]; theta[x_] := If [ x < 0 , 0 , 1]; F[y_] := Integrate [ theta[ Sin[x] ], { x , 0 , y } ]; Plot[F[y] , { y , -4 Pi , 4 Pi }]; Take y = -5 Plot[Sin[x], {x, 0, -5}]; Plot[theta[Sin[x]], {x, 0, -5}]; Integrate [ theta[ Sin[x] ], { x , 0 , -5 } ] 0 Clearly the above integral is wrong. Integrate [ theta[ Sin[x] ], { x , -Pi , -5 } ] -5 + Pi Integrate [ theta[ Sin[x] ], { x , 0 , -Pi } ] 0 Assume that the problem arises in trying to work with the given definition of theta. Redefine theta as Clear[theta]; theta[x_ /; x == 0] := 1; theta[x_] := (Sign[x] + 1)/2; Then Plot[F[y] , { y , -4 Pi , 4 Pi }]; Bob Hanlon In a message dated 1/16/2000 5:24:21 AM, naum at cava.physics.ucsb.edu writes: > 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. >