[Date Index]
[Thread Index]
[Author Index]
Re: Bug in NIntegrate[]?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg126893] Re: Bug in NIntegrate[]?
*From*: A Retey <albert.retey at gmail.com>
*Date*: Fri, 15 Jun 2012 15:29:51 -0400 (EDT)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*References*: <jrep0q$nrh$1@smc.vnet.net>
Hi,
> 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
Another variant of the most frequently asked question :-). NIntegrate does evaluate the integrand symbolically, if not told otherwise. That symbolic evaluation will return 1 in your case:
In:=f[x]
Out:= 1
Since NIntegrate doesn't seem to accept the option Evaluated->False as some other functions which have the same problem do, you need to define the function so it only evaluates for numeric arguments:
ClearAll@f
f[x_?NumericQ] := 0 /; x < 0 || x > 1;
f[x_?NumericQ] := 1
That will make NIntegrate behave as expected (it will complain about bad convergence, but that I'd consider expected behaviour for that function :-). Note that it can do better if you use more "mathematical" ways to define your function, e.g. UnitStep, UnitBox or HeavsideTheta.
hth,
albert
Prev by Date:
**Re: Bug in NIntegrate[]?**
Next by Date:
**Re: Bug in NIntegrate[]?**
Previous by thread:
**Re: Bug in NIntegrate[]?**
Next by thread:
**Re: Bug in NIntegrate[]?**
| |