Solution:
If we partitionthe interval into equalsub-intervals,then each sub-intervalwill have length
and height as variesfrom to So we have and
Since , we then haveby substitution
as. Hencethe area is
This examplemay also be solvedwith simplegeometry. It is left to the readerto confirmthat the two methods
yield the samearea.
LessonSummary
- We usedsigmanotationto evaluatesumsof rectangularareas.
- We foundlimitsof upperand lowersums.