2. Find critical curves for the following functionals, where in each case x(0) = 0 and x(1) = 1: (a) I(x) = So x'(t) at. (b) I(x) = So x(t)x' (t) dt. (c) I(x) = So (x(t) + tx'(t))dt. (See the Exercise on page 2.3.)