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Integrating to an absolute value?

  1. Oct 17, 2012 #1
    1. The problem statement, all variables and given/known data
    I need some help understanding an integral step in the example below. I get how the integrand was set up, but I don't get how comes to two expressions with the absolute value of z-L/2.

    (Problem description if that is needed: L is the length of a cylinder with radius R, and P is the polarization of the cylinder in direction of its length. Calculate the electric field at a point on the axis of the rod)

    2. Relevant equations

    http://imageshack.us/a/img594/1895/absolutevalue.png [Broken]

    3. The attempt at a solution
    I don't understand that step really. Google has no answers. I thought that it might have been some absolute value identities, but it seems that was not the case. Is there someone who'd lend a hand?
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Oct 17, 2012 #2

    Ray Vickson

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    [tex] \int_0^R \frac{r}{\sqrt{r^2+a^2}} dr
    = \frac{1}{2} \int_{r=0}^R \frac{d(r^2)}{\sqrt{r^2+a^2}}
    = \frac{1}{2} \int_0^{R^2} \frac{dy}{\sqrt{y+a^2}} = \left. \sqrt{y+a^2}\right|_0^{R^2}[/tex] Look at what you get if a > 0 or a < 0.

    RGV
     
    Last edited by a moderator: May 6, 2017
  4. Oct 17, 2012 #3

    SammyS

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    It's because, [itex]\displaystyle \sqrt{u^2}=|u|\ .[/itex]
     
    Last edited by a moderator: May 6, 2017
  5. Oct 18, 2012 #4
    Wow thank you. That was pretty helpful
     
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