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