(5.2) Consider the integral 2 1 I = 2 ( x 2 + y2 ) dt, and the 1-parameter transformation x = x cosa + y sin a, y = y cosa - x sina, t = t. (a) Show that the given integral I is invariant under the given 1-parameter transformation. (6) (b) Use Noether's theorem and part (5.2(a)) to show that xy - xy is constant along an extremal of (6) the Lagrangian L( x, y ) =