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Re: Bug in NIntegrate[]?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126900] Re: Bug in NIntegrate[]?
  • From: Sseziwa Mukasa <mukasa at gmail.com>
  • Date: Fri, 15 Jun 2012 15:32:16 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201206150741.DAA24405@smc.vnet.net>

You ran into the issue of calling f with a non-numeric argument, there are still issues due to the discontinuities but:

(Debug) In[14]:= f[x_?NumericQ]:=0/;x<0||x>1
f[x_?NumericQ]:=1
(Debug) In[16]:= NIntegrate[f[x],{x,-1,2}]
(Debug) During evaluation of In[16]:= NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >>
(Debug) During evaluation of In[16]:= NIntegrate::ncvb: NIntegrate 
failed to converge to prescribed accuracy after 9 recursive bisections in x near {x}  {1.00386}. NIntegrate obtained 0.9995253309911655` and 0.0007611273421692226` for the integral and error estimates. >>
(Debug) Out[16]= 0.999525

Regards,
	Ssezi

On Jun 15, 2012, at 3:41 AM, GS 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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