This paper is concerned with the controllability of the linear Korteweg de Vries equation on the domain Omega = (0, +infinity), the control being applied at the left endpoint x = 0. It is shown that the exact boundary controllability holds true in L-2 (0, +infinity) provided that the solutions are not required to be in L-infinity (0, T, L-2 (0, +infinity)). The proof rests on Carleman's estimate and an approximation theorem. A similar result is obtained for the heat equation and for the Schrodinger equation.