Electronic Journal of Differential Equations, Conference 06 (2001), pp. 297-301. Title: On the Opial-Olech-Beesack inequalities. Authors: William C. Troy (Univ. of Pittsburgh, Pittsburgh, Pa, USA) Abstract: We investigate two integral inequalities. The first of these generalizes a result proved by Beesack \cite{beesack} in 1962. We then use our inequality to generalize earlier results of Olech \cite{olech} and Opial \cite{opial} on a related problem. Published January 8, 2001. Math Subject Classifications: 41A44, 58E35. Key Words: Schwarz inequality; integral inequalities.