Albert Barnes on Acts 13:36

For David, etc. This verse is designed to show that the passage in Ps 16 could not refer to David, and must therefore relate to some other person. In Acts 13:37, it is affirmed that this could refer to no one, in fact, but to the Lord Jesus.

After he had served his own generation. See the margin. Syriac, "David in his own generation having served the will of God, and slept," etc. Arabic, "David served in his own age, and saw God." The margin probably most correctly expresses the sense of the passage. To serve a generation, or an age, is an unusual and almost unintelligible expression.

Fell of sleep. Greek, slept; that is, died. This is the usual word to denote the death of saints. It is used of David in 1Kgs 2:10. Mt 27:52.

And was laid unto, etc. And was buried with his fathers, etc., 1Kgs 2:10.

And saw corruption. Remained in the grave, and returned to his native dust. See this point argued more at length by Peter, in Acts 2:29-32, and explained Acts 2:29, and Acts 2:30-30.

(2) "after he had served" "after he had in his own age served the will of God"

(d) "fell on sleep" 1Kgs 2:10 (+) "laid" "gathered"