Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I'm reading the following paper:

http://prola.aps.org/abstract/PR/v127/i6/p1918_1

(It's physics, you don't really have to click that)

Somewhere along the way the authors make a transition that I can't understand. Basically they have an ODE (5.9), which is integrated to give equation (5.10). Then they define a new function, y^{2}, to replace the original function, v^{2}, and find a new integral equation for it (5.14). I'm bringing two screen shots from the article that show this transition. The only other thing you need to know is that v^{2}_{a}, v^{2}_{b}and v^{2}_{c}are the roots of the expression insider the root in the integral of (5.10).

Screen shots: (in order)

http://img59.imageshack.us/img59/1887/partajj6.png [Broken]

http://img62.imageshack.us/img62/5359/partbyc9.png [Broken]

Now, I tried following this transition myself and couldn't make any sense of it. Most of all, I don't understand how the final integral equation (5.14) has y in the limits of integration, and not y^{2}or something like that.

Help, please?

Thanks,

Chen

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# Changing variables in integrals?

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