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 .