Integrate substraction of squareroots

[Blastrix91]

Homework Statement

I'm having some troubles with my calculus. I can't get from the first step to the second step in the example below:

Homework Equations

http://img853.imageshack.us/img853/4350/unavngivetpn.png

The Attempt at a Solution

$$\int_{-L/2}^{L/2} [R^2 + (Z-Z_0)^2]^{1/2} - \int_{-L/2}^{L/2} [(Z-Z_0)^2]^{1/2}$$

The last term I have calculated to be $-Z_0 L$ which matches the solution. The first term however I'm having some problems with. Is trig substitution necessary here?

 

[I like Serena]

Hi Blastrix91!

I recommend using a table of integrals, like the one here on wiki: http://en.wikipedia.org/wiki/List_of_integrals_of_irrational_functions

The first integral is the one you need.
If you want you can take the derivative of its right hand side to see that it is indeed the integral expression.

 

[Dick]

And, yes, to derive the result in the table you want a trig or hyperbolic trig substitution.