We are concerned with the problem of solving the integral equation of the first kind \(Tx=y\) , where T is an integral operator, a prototype of an ill-posed problem. Discretization and regularization are needed to derive a stable approximation of the solution. The operator T may be approximated by a sequence of finite rank operators \(T_n\) and then the regularization procedure is applied. The discretization procedure may be applied after the regularization procedure. In this paper, we compare both approaches, theoretically and numerically.