This is a past examination question. Let n 3 1 he an integer, let 5]. to is given by a stationary path of the Lagrangian functional (3: [x] =1 1dttgsnx), x(0) = x0, x[t1) = x1, 0 where L = T V and T is the total kinetic energy Using the above rst-integral, show that= if V is independent of t, the total energy E = T + V of the particle is a constant of the motion. mks: HIGH1 Now consider the case V[t,:r1,...,:5:n)= Z Edi-(tmaarj), where, for each pair 1', j, the function lrj is a smooth potential function. Using Noether's theorem, show that the linear momentum 211:1 mimi- is a constant of the motion of the particles