Re: Integration of very simple partwise definded functions fails

*To*: mathgroup at smc.vnet.net*Subject*: [mg15807] Re: [mg15720] Integration of very simple partwise definded functions fails*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>*Date*: Sun, 7 Feb 1999 02:04:22 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

On Fri, Feb 5, 1999, D.O. <oberfeld at psych.gp.TU-Berlin.DE> wrote: >Hi, > >I was quite surprised that Mathematica will not evaluate any Integrals >of simple functions like > >f[x_/;x<=2]:=1 >f[x_/;x>2]:=2 > >Integrate[f[x],{x,0,1}] > > >NIntegrate also complains about singularities. > >Do I miss something? There must be a fast way out... > >Thanks for all suggestions! > > >Daniel Oberfeld >Institut fuer Psychologie >Allgemeine Psychologie >TU Berlin >FS1, Raum FS105 >Franklinstr. 5-7 >10587 Berlin >T. 030/314-79541 >Fax. 030/314-25996 NIntegrate works fine, but you need to assign a value at 2. f[2]:= 3 (for example) will do as well as any other real number: In[29]:= NIntegrate[f[x],{x,0,1}] Out[29]= 1. with no complaints. It is true that Integrate (rather than NIntegrate) does not work for a piecewise function defined in this way, but you can make it work by using an If based definition: In[35]:= g=Function[x,If[x<2,1,2]]; In[36]:= Integrate[g[x],{x,0,1}] Out[36]= 1 Andrzej Kozlowski Toyama International University JAPAN http://sigma.tuins.ac.jp/ http://eri2.tuins.ac.jp/