Question

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.

Answer 1

To find the optimal path between the points (0,0) and (1,0) that bounds an area of A, we can use the Euler-Lagrange equation. The Euler-Lagrange equation is a differential equation used to find the extremum of a functional.

Step-by-step explanation:

To find the optimal path between the points (0,0) and (1,0) that bounds an area of A, we can use the Euler-Lagrange equation. The Euler-Lagrange equation is a differential equation used to find the extremum of a functional. In this case, we want to find the path that minimizes the total area under the curve. The Euler-Lagrange equation is given by:

d2y/dx2 = 0

We can solve this second-order linear differential equation to find the optimal path which lies on or above the x-axis.