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MathGroup Archive 2004

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Re: Integrating UnitSteps

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48796] Re: Integrating UnitSteps
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Wed, 16 Jun 2004 07:48:57 -0400 (EDT)
  • Organization: The University of Western Australia
  • References: <cap3m9$cab$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <cap3m9$cab$1 at smc.vnet.net>, BZ <BZ at caradhras.net> wrote:

> Hi guys!
> 
> I'm trying to integrate a function that has a discontinuity at a
> single point.  I'm using UnitStep to do this, but it doesn't work very
> well.  To illustrate this, a simple example (my real function is much
> more complicated than this):
> 
> In[1]:= Integrate[1/x^2, {x, b, Infinity}]
> 
>         1
> Out[1]= -
>         b
> 
> Ok, so far so good, but now let's add a discontinuity at x=1:
> 
> 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}]]

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul


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