When samples are drawn for the determination of the AUC, it may be impossible to quantify drug concentrations in some samples during the terminal elimination phase because the concentrations are below the sensitivity of the analytical assay. However, the drug is still present in plasma and is contributing to the total AUC. So, the area under the tail of the curve has to be estimated and added to the calculation of the total AUC.
When the last concentration drawn is during the elimination phase of the drug, the concentration at any time after this last concentration will be:
Integrating the concentration from time of the last sample to infinity to calculate the area under the tail:
Cp last
k