Integration of dirac delta composed of function of integration variable
Hi all,
I'm working through Chandrasekhar's Stochastic Problems in Physics and Astronomy and can not understand the steps to progress through Eq. (66) in Chapter 1. The integral is: [tex]\prod^{N}_{j=1} \frac{1}{l^{3}_{j}\rho}\int^{\infty}_{0} sin(\rhor_{j})r_{j}\delta (r^{2}_{j}l^{2}_{j})dr_{j} = \prod^{N}_{j=1} \frac{sin(\rhol_{j})}{\rhol_{j}}[/tex] Could anyone show the steps on how this result was obtained? I am aware of how to simplify a dirac delta that is composed of a function, but it does not lead me to the above result. Thanks. kmd 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 
Re: Integration of dirac delta composed of function of integration variable
Weird, I didn't get that one either. I got
[tex]\prod^{N}_{j=1} \frac{sin(\rhol_{j})}{2\rhol_{j}^3}[/tex] 
Re: Integration of dirac delta composed of function of integration variable
Quote:

Re: Integration of dirac delta composed of function of integration variable
Yes, you are right about the units. And someone else aside from myself got phsopher's result as well.
A few equations back, the author defines the probability distribution that he is using, and if I integrate over all angles and radial distances, I don't get unity. I think there are significant typos in this section. Thanks for the help. kmd 
All times are GMT 5. The time now is 12:22 PM. 
Powered by vBulletin Copyright ©2000  2014, Jelsoft Enterprises Ltd.
© 2014 Physics Forums