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MathGroup Archive 2000

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Re: Integrate with If

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22361] Re: [mg22180] Integrate with If
  • From: bergervo at prl.philips.nl (Bergervoet J.R.M.)
  • Date: Fri, 25 Feb 2000 21:14:13 -0500 (EST)
  • Organization: Philips Research Laboratories Eindhoven, Netherlands
  • References: <200002170624.BAA04409@smc.vnet.net> <88jt51$9lf@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In <88jt51$9lf at smc.vnet.net> Hartmut Wolf <hwolf at debis.com> writes:

>> Why does
>> 
>>         Integrate[If[Sin[t] > 0, 1, 0] , {t, -Pi, Pi}]
>> 

>Integrate doesn't work with If, use UnitStep instead. So both

>In[17]:= Plot[UnitStep[t], {t, -Pi, Pi}]
>Out[17]= Graphics[]

>In[18]:= Integrate[UnitStep[t], {t, -Pi, Pi}]
>Out[18]= Pi

>do well.

But this functionallity (in order to generalize to functions other than
Sin[]) would require:

  Integrate[UnitStep[Sin[t]], {t,-Pi, Pi}]

and that still gives 0 (incorrect!). It does work with jump-point 0:

  Integrate[UnitStep[Sin[t]], {t,-Pi, 0, Pi}]

which correctly gives Pi.

(Jos)

--
  Dr. Jozef R. Bergervoet                      Electromagnetism and EMC
  Philips Research Laboratories,             Eindhoven, The Netherlands
  Building WS01                                     FAX: +31-40-2742224
  E-mail: bergervo at natlab.research.philips.com    Phone: +31-40-2742403



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