Re: Integrate with If

*To*: mathgroup at smc.vnet.net*Subject*: [mg22200] Re: [mg22180] Integrate with If*From*: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>*Date*: Fri, 18 Feb 2000 02:34:36 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

on 00.2.17 3:24 PM, Johan Berglind,5879 at johanbe at chl.chalmers.se wrote: > Why does > > Integrate[If[Sin[t] > 0, 1, 0] , {t, -Pi, Pi}] > > evaluate to 2Pi? > > Plot[If[Sin[t] > 0, 1, 0] , {t, -Pi, Pi} ] > > looks all right. > > > Puzzled, > > Johan Berglind, > Chalmers, Goteborg, > Sweden. > This is of course wrong but I would not in general recommend trying this sort of thing. When you use Integrate Mathematica has to find an anti-derivative and in this case the antiderivative has a jump at 0. Integrate is not very good at dealing with singularities. In some cases like this one you can deal with this problem by adding the jump point to the range of integration as in : In[15]:= Integrate[If[Sin[t] > 0, 1, 0] , {t, -Pi, 0, Pi}] Out[15]= Pi Or if you are satisfied with a numerical answer use NIntegrate: In[16]:= NIntegrate[If[Sin[t] > 0, 1, 0] , {t, -Pi, Pi}] Out[16]= 3.14159