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