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

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  • Subject: [mg91639] Re: How to Integrate[Abs[x]]?
  • From: Bill Rowe <readnews at>
  • Date: Sat, 30 Aug 2008 01:52:16 -0400 (EDT)

On 8/29/08 at 4:25 AM, lobais at (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?

Your TI calculator undoubtedly assumes the domain of x to be
real numbers. Mathematica by default assumes the domain of x to
be complex numbers. And that is why no solution to the integral
is returned. You can restrict x to be a real number by using
Assuming. For example,

In[2]:= Assuming[x \[Element] Reals, Integrate[Abs[x], x]]

Out[2]= Piecewise[{{-(x^2/2), x <= 0}}, x^2/2]

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