Let a, b, A be a positive number we’ve been given. Consider the problem of finding the shortest path between the points (0,0) and (1,0) such that the region bounded by the vertical lines x= 0, x= 1, the x-axis, and the curve formed by the path has total area A. Identify the Euler-Lagrange equation and use this to find the optimal path which lies on or above the x-axis. Hint: Can you obtain an equation of the form u′(x) =f(x)?

*This is the entirety of the question with the hint included.