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
The University of Western Australia      (CRICOS Provider No 00126G)
35 Stirling Highway
Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

```

• Prev by Date: Re: exporting the values of evaluated functions
• Next by Date: Re: Integrating UnitSteps
• Previous by thread: Re: Integrating UnitSteps
• Next by thread: Re: Integrating UnitSteps