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Re: ..Integrate[Abs[x]... UnitStep again!

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  • Subject: [mg23728] Re: [mg23712] ..Integrate[Abs[x]... UnitStep again!
  • From: "Mark Harder" <harderm at>
  • Date: Mon, 5 Jun 2000 01:09:20 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

    It occured to me that Abs[x]= Integrate[Sign[x],x]; but when I tried
that, Mathematica generated an "invalid integration limit or variable..."
error, so I split the function in two parts joining at x=0 using the Unit
Step function & that worked:

mySign = UnitStep[t] - UnitStep[-t];
Plot[dublStep, {t, -2, 2} ]

(* output omitted   *)

myAbs = Integrate[mySign, t]
Plot[myAbs, {t, -3, 3}]

-t + 2 t UnitStep[t]
(*   Plot omitted   *)

Integrate[myAbs, t]
Plot[%, {t, -4, 4}]

-t^2/2 + t^2 UnitStep[t]
(*   Plot omitted   *)

-mark harder
harderm at

-----Original Message-----
From: José María Lasso <jml at>
To: mathgroup at
Subject: [mg23728] [mg23712] Thx for your help

>Thx for the answers to my last post, but I have a new question, similar to
>the last one, when I try: Integrate[Abs[x],x], there is no result, just the
>original input, what I am doing wrong?, I need some advice about a good
>book about Mathematica for beginers.Thx again.Best regards
>Jose M Lasso

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