Piecewise functions definition and usage

• To: mathgroup at smc.vnet.net
• Subject: [mg24098] Piecewise functions definition and usage
• From: Viorel Ontalus <vio2 at mail.lehigh.edu>
• Date: Tue, 27 Jun 2000 00:51:54 -0400 (EDT)
• Organization: Lehigh University
• Sender: owner-wri-mathgroup at wolfram.com

```It seems I got into an area where Mathematica has some problems, and I
hope somebody can give me a hint on how to go around these problems.

1.  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 !!

2. For fun I tried the only reference from the book on piecewise
functions:
If[Abs[x-3]<10, f[x_]:=Sqrt[1- ( (x-3)/10)^2  ] , f[x_]:=0 ]

This definition does not work !!

```

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