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