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An integral of the form : $$\int_a^b \sqrt{\frac {1+|y'(x)|^2}{2g(x-a)+v_a^2}}dx$$

The above integral is the Time taken for an object to fall under the action of gravity with some particular tragectory . I am trying to differentiate it wrt $y'$ in order to put the values in Euler lagrange equation and get the first variation.

I am confused with fact that $y'$ has a modulus . Can some one give me suggestions and help . Thanks P.S any other idea and explanations are very much welcome .

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    Differentiate it *wrt $y'$'*??2012-10-24
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    @Berci: Yes , wrt is with respect to y' . Or any other ideas are welcome to find the first variation.2012-10-24
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    Note that $|a|^2=a^2$ for all $a\in\mathbb R$.2012-10-24

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