       RE: Integration of very simple partwise defined functions fails

• To: mathgroup at smc.vnet.net
• Subject: [mg15775] RE: [mg15720] Integration of very simple partwise defined functions fails
• From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
• Date: Sun, 7 Feb 1999 02:03:53 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Daniel Oberfeld  wrote:
___________________

I was quite surprised that Mathematica will not evaluate any Integrals
of simple functions like

f[x_/;x<=2]:=1
f[x_/;x>2]:=2

Integrate[f[x],{x,0,1}]

Do I miss something? There must be a fast way out...

________________

I don't know what you can do to get Integrate to deal with this.   But
NIntegrate[f,{x,x0,x1,x2,...xi,xj}]effectively breaks up the integral
into
pieces along [x0,x1], [x1,x2], ...,[x,xi].  So include the point of
discontinuity in the range of integration.

In:=
NIntegrate[f[x],{x,0,2,5}]
Out=
8.

If you don't know where the discontinuities are you can write some code
that does it by using NDSolve on the equivalent Diff. Eq.

In:=
NIntegrate2[f_,{x_,a_,b_}]:=
Module[{y},
y[b]/.NDSolve[{y'[x]==f,y[a]==0},y,{x,a,b}][]
]

In:=
NIntegrate2[f[x],{x,0,5}]
Out=
8.00001

Regards,
Ted Ersek

```

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