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Re: Bug in NIntegrate[]?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg126904] Re: Bug in NIntegrate[]?
*From*: Bob Hanlon <hanlonr357 at gmail.com>
*Date*: Fri, 15 Jun 2012 15:33:39 -0400 (EDT)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*References*: <201206150741.DAA24405@smc.vnet.net>
NIntegrate first tries to evaluate its argument symbolically and evaluates to 1 since your definition defines f as one for symbolic input.
You could change your default to
f[x_?NumericQ] = 1;
to preclude evaluation for symbolic input; however, it would be better to define f using Piecewise.
f[x_] := Piecewise[{{1, 0 <= x <= 1}}]
Bob Hanlon
On Jun 15, 2012, at 3:41 AM, GS <vokaputs at gmail.com> wrote:
> I define the function f[x] as follows:
>
> f[x_] := 0 /; x < 0 || x > 1;
> f[x_] := 1
>
> It is zero outside of the interval [0,1]. This can be verified by plotting
> Plot[f[x], {x, -1, 2}]
>
> Now I integrate it from -1 to 2:
> In[270]:= NIntegrate[f[x], {x, -1, 2}]
> Out[270]= 3.
>
> The result should be 1, but it is 3. Clearly Mathematica ignores the fact that f[x] is zero outside of [0,1].
>
> This caused a lot of headache for me recently when I encountered such behavior in one of my research code.
> GS
>
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