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MathGroup Archive 2000

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Re: Piecewise functions definition and usage

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24130] Re: [mg24098] Piecewise functions definition and usage
  • From: BobHanlon at aol.com
  • Date: Wed, 28 Jun 2000 02:11:48 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 6/27/2000 1:06:55 AM, vio2 at mail.lehigh.edu writes:

>I am trying to define a piecewise function and do some computations
>with it. When I integrate mathematica does not behave. Here is an simple
>example you can run and see what I am talking about
>
>Clear[f,x}
>f[x_] := Sqrt[ 1- ( (x-3)/10)^2  ] /;
>Abs[x-3]<10
>f[x_] := 0 /;
>Abs[x-3]>3 ;          (*this is a very simple piecewise function but one
>must be sure the Sqrt is from a positive # )
>
>NIntegrate[f[x],{x,-1,17}]   (* Here Mathematica goes nuts !!!*)
>
>Of course it gives an answer but if your program is more complex, then
>you never get an answer !!
>( I tried to make the upper limit a variable  etc !!)
>Does anybody know how to avoid the error , or non convergence messages
>I get !!
>

Needs["Algebra`InequalitySolve`"]

InequalitySolve[Abs[x - 3] < 10, x]

-7 < x < 13

f[x_] := Sqrt[ 
      1 - ( (x - 3)/10)^2  ] * (UnitStep[(x + 7)] - UnitStep[(x - 13)])

Plot[f[x], {x, -10, 15}, 
    PlotStyle -> {AbsoluteThickness[2], RGBColor[1, 0, 0]}];

Integrate[f[x], {x, -1, 17}]

(2*Sqrt[21])/5 + (5*Pi)/2 + 5*ArcSin[2/5]

% // N

11.74459614229426

Bob Hanlon


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