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