What is the physical meaning of integrating the output characteristic of a MOSFET?
If you take any point in the \$ V_{ds} \$ - \$I_{ds}\$ curve, you get the instantaneous power dissipation across the drain-source junction of the MOSTET for the given { \${V_{ds}, I_{ds}, V_{gs}}\$}. But if you integrate the curve, you get the area under the curve mathematically, which I don't think suggests any useful physical quantity to measure.