       Re: How to Integrate[Abs[x]]?

• To: mathgroup at smc.vnet.net
• Subject: [mg91644] Re: [mg91624] How to Integrate[Abs[x]]?
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sat, 30 Aug 2008 01:53:11 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200808290825.EAA24127@smc.vnet.net>

```You could use either of the following:

Integrate[Abs[x], x, Assumptions -> x \[Element] Reals] // InputForm
Piecewise[{{-x^2/2, x <= 0}}, x^2/2]

g[x_]=Piecewise[{{x,x>=0},{-x,x<0}}]
Integrate[g[x],x] // InputForm
Piecewise[{{-x^2/2, x <= 0}}, x^2/2]

(In both cases I used InputForm for the answer since it's awkward to
reproduce the 2D  Piecewise output in linear e-mail text.)

Of course if you have a definite integral, there's no difficulty using
Abs[x] directly, e.g.:

Integrate[Abs[x],{x,-2,1}]
5/2

Thomas Dybdahl Ahle wrote:
> On my Ti calculater |x| is easily integrated to |x|*x/2, but when I type Integrate[Abs[x],x] in mathematica, it seams like it can't find the solution.
> Is there anything I'll have to do, to make mathematica find the solution?
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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