Integrating UnitSteps

• To: mathgroup at smc.vnet.net
• Subject: [mg48779] Integrating UnitSteps
• From: BZ <BZ at caradhras.net>
• Date: Wed, 16 Jun 2004 04:54:40 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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

```

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