# Integrating to an absolute value?

1. Oct 17, 2012

### Blastrix91

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. Oct 17, 2012

### Ray Vickson

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

RGV

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

### SammyS

Staff Emeritus
It's because, $\displaystyle \sqrt{u^2}=|u|\ .$

Last edited by a moderator: May 6, 2017
4. Oct 18, 2012

### Blastrix91

Wow thank you. That was pretty helpful