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MathGroup Archive 2004

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Re: Integrating UnitSteps

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48801] Re: Integrating UnitSteps
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Wed, 16 Jun 2004 07:49:05 -0400 (EDT)
  • References: <cap3m9$cab$1@smc.vnet.net> <paul-517690.18014516062004@news.uwa.edu.au> <20040616100735.GA6864@matilda.phys.uu.nl>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Bas:

>You wrote:
>
>>  > In[2]:= Integrate[UnitStep[x - 1]/x^2, {x, b, Infinity}]
>>  >
>>  >                                UnitStep[-1 + x]
>>  > Out[2]= If[b < 1, 1, Integrate[----------------, {x, b, Infinity}]]
>>  >                                        2
>>  >                                       x
>>  >
>>  > Which is correct, in principle.  However, I'm trying to get an
>>  > explicit expression for b>1:
>>
>>  Then you can pass this assumption to the Mathematica integrator:
>>
>  >   Assuming[b > 1, Integrate[UnitStep[x - 1]/x^2, {x, b, Infinity}]]
>
>Unfortunately, that doesn't work:
>
>In[1]:=  Assuming[b > 1, Integrate[UnitStep[x - 1]/x^2, {x, b, Infinity}]]
>
>Out[1]= Assuming[b > 1, If[b < 1, 1,
>
>                 UnitStep[-1 + x]
>>      Integrate[----------------, {x, b, Infinity}]]]
>                         2
>                        x

It works for me:

In[1]:= $Version
Out[1]= "5.0 for Mac OS X (June 10, 2003)"

In[2]:= Assuming[b > 1, Integrate[UnitStep[x - 1]/x^2, {x, b, Infinity}]]

Out[2]= 1/b

Cheers,
Paul


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