RE: Integrating UnitSteps
- To: mathgroup at smc.vnet.net
- Subject: [mg48806] RE: [mg48779] Integrating UnitSteps
- From: "David Park" <djmp at earthlink.net>
- Date: Thu, 17 Jun 2004 04:07:18 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Use the Assumptions option in Integrate.
Integrate[UnitStep[x - 1]/x^2, {x, b, Infinity}, Assumptions -> b > 1]
1/b
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: BZ [mailto:BZ at caradhras.net]
To: mathgroup 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