1. (5 points) Find the extremal of the functional
subject to the boundary conditions
2. (5 points) Find the extremal of the functional
How many boundary conditions do you need to specify at the two endpoints to determine the extremal uniquely?
3. (5 points)Find the extremal of the functional
subject to the conditions y(0) = 0,y(1) = 0 and the constraint , where A is a given constant. You need to find the Lagrange multiplier as a function of A and cannot leave your answer in terms of the Lagrange multiplier.
