Boolean Integral

• To: mathgroup at smc.vnet.net
• Subject: [mg62357] Boolean Integral
• From: "Brambilla Roberto Luigi (CESI-PGE)" <RLBRAMBILLA at cesi.it>
• Date: Tue, 22 Nov 2005 04:41:58 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

I have defined the following support function:

chi[func_,y1_,y2_]:=Boole[yi<func<y2]

that gives 1 if yi<func<y2 and 0 otherwise. It works well with Plot :

(*example*)
foo[x_]:=-BesselJ[1,x]
y1=.12;
y2=.16;
Plot[{foo[x],chi[foo[x]],y1,y2],y1,y2},{x,0,20},
PlotRange->All,PlotStyle->{Black,Red,Blue,Blue}]

but if I want to *measure* the sum of intervals where y1<foo<y2, the answer is wrong:  the integral

NIntegrate[chi[foo[x],y1,y2],{x,0,20}]

often gives 0 since x-sample points (Gauss points) of a numerical method may fall into intervals where chi=0.
If I use Method->MonteCarlo the results is rather slow (10 sec.) and change a little bit at every execution

NIntegrate[chi[foo[x],y1,y2],{x,0,20},Method->MonteCarlo]
1.3668

There are other NIntegrate settings to obtain the wright result more quicly?
(I would like to avoid to use FindRoot and to fragment the integral etc...)

Any help well accepted.
Thank You.
Rob.

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```

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