Re: Integrating UnitSteps
- To: mathgroup at smc.vnet.net
- Subject: [mg48799] Re: Integrating UnitSteps
- From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig-de>
- Date: Wed, 16 Jun 2004 07:49:00 -0400 (EDT)
- Organization: Uni Leipzig
- References: <cap3m9$cab$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
Integrate[UnitStep[x - 1]/x^2, {x, b, Infinity}, Assumptions -> {b > 0}]
Regards
Jens
"BZ" <BZ at caradhras.net> schrieb im Newsbeitrag
news:cap3m9$cab$1 at smc.vnet.net...
> 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:
>
> In[3]:= FullSimplify[%, b > 1]
>
> UnitStep[-1 + x]
> Out[3]= If[b < 1, 1, Integrate[----------------, {x, b, Infinity}]]
> 2
> x
>
> Why isn't this expression simplified? Why doesn't Mathematica
> evaluate the Integration inside the If[] (the UnitStep is 1 there
> anyway)? Should I be using UnitSteps at all for these kinds of
> functions?
>
> --
> BZ
>