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>
- Reply-to: murray at math.umass.edu
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
- References:
- How to Integrate[Abs[x]]?
- From: Thomas Dybdahl Ahle <lobais@gmail.com>
- How to Integrate[Abs[x]]?