Suppose for Thenthe errorestimateis givenby
Example3:
a. Use Simpson’s Rule to approximate with.
Solution:
We find
This turnsout to be a prettygoodestimate,sincewe knowthat
Thereforethe erroris less than.
b. Find so that the SimpsonRule Estimatefor is accurateto
Solution:
We needto find suchthat We startby notingthat for
Hencewe can take to find our errorbound:
Hencewe needto solvethe followinginequalityfor :