We can re-writethis resultas:
We observethat as
We now are able to definethe area undera curveas a limit.
Definition:Let be a continuousfunctionon a closedinterval Let be a partitionof equalsub
intervalsover Thenthe area underthe curveof is the limit of the upperand lowersums,that is
Example3:
Use the limit definitionof area to find the area underthe function from to