The pressure-volume work for an ideal gas can be calculated by using the expression $W = - \int\limits^{V_{f}}_{V_i} P_{ex} \,dV$. The work can also be calculated from the $PV -$ plot by using the area under the curve within the specified limits. When an ideal gas is compressed $(i)$ reversibly or $(ii)$ irreversibly from volume $V_i$ to $V_f$. Choose the correct option.