Integrating to an absolute value?

  • Thread starter Blastrix91
  • Start date
  • #1
25
0

Homework Statement


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)

Homework Equations



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

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:

Answers and Replies

  • #2
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,722

Homework Statement


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)

Homework Equations



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

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?

[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:
  • #3
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,365
1,033

Homework Statement


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)

Homework Equations



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

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?

It's because, [itex]\displaystyle \sqrt{u^2}=|u|\ .[/itex]
 
Last edited by a moderator:
  • #4
25
0
Wow thank you. That was pretty helpful
 

Related Threads on Integrating to an absolute value?

Replies
5
Views
2K
  • Last Post
Replies
2
Views
10K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
857
  • Last Post
Replies
1
Views
830
  • Last Post
Replies
1
Views
3K
Replies
2
Views
9K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
2K
Top