Iím practicing some problems for applied mathematics, and couldnít quite solve the following:
In calculus of variations, if the speed is x, and the travel time is t = Integral(0 to 1) (1/x)Sqrt(1+(uí)≤)dx with u(0)=0 and u(1)=1, how can see from the Euler equation that uí/x(sqrt(1+(uí)≤)) is constant?
And how can I integrate once more in order to get the optimal path u(x)?
If you know the solution, or could guide me in the right direction, I would appreciate it a lot! Thanks in advance..