How will you calculate the work done on an ideal gas during compression,when the change in pressure is carried out in infinite steps?

$A$ process or change is said to be reversible if it is carried out in such a way that the process could,at any moment,be reversed by an infinitesimal change.
When pressure changes in infinite steps (reversible conditions) during compression from an initial volume $V_i$ to a final volume $V_f$,the work done can be calculated by integrating the pressure with respect to volume:
$w = -\int_{V_i}^{V_f} p_{ext} \, dV$
In a $pV$-plot,this work done on the gas is represented by the area under the curve between $V_i$ and $V_f$.