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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.
>
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