Two integral versions of input to state stability are considered: integral input-to-state stability (iISS) and integral input-to-integral-state stability (iIiSS). We present sufficient conditions that guarantee that if a controller achieves semiglobal practical iISS (respectively, iIiSS) of an approximate discrete-time model of a nonlinear sampled-data system, then the same controller achieves semiglobal practical iISS (respectively, iIiSS) of the exact discrete-time model by reducing the sampling period. Recent results on numerical methods for systems with measurable disturbances can be used to generate approximate models that we consider. Results are presented for arbitrary dynamic controllers that can be discontinuous in general.