-- Feynman and Hibbs problem 2-3 "Verify equation (4)" A = f / (2 m) B = (xb - xa) / (tb - ta) - f (tb^2 - ta^2) / (2 m (tb - ta)) C = f (ta tb^2 - ta^2 tb) / (2 m (tb - ta)) + (tb xa - ta xb) / (tb - ta) x = A t^2 + B t + C check(d(x,t,t) == f / m) check(eval(x,t,ta) == xa) check(eval(x,t,tb) == xb) "ok" "Verify equation (5)" ta = 0 tb = T A = f / (2 m) B = (xb - xa) / T - f T / (2 m) C = xa check(x == A t^2 + B t + C) "ok" "Verify equation (6)" v = d(x,t) check(v == f t / m - f T / (2 m) + (xb - xa) / T) "ok" "Verify equation (7)" L = 1/2 m v^2 + f x A = f^2 / m B = 2 f (xb - xa) / T - f^2 T / m C = f^2 T^2 / (8 m) + f (3 xa - xb) / 2 + m (xb - xa)^2 / (2 T^2) check(L == A t^2 + B t + C) "ok" "Verify equation (8)" S = defint(L, t, 0, T) check(S == m (xb - xa)^2 / (2 T) + f T (xb + xa) / 2 - f^2 T^3 / (24 m)) "ok" Run