CK12 Calculus - Single Variable

We can use the notationto indicateusefulformulasthat we will haveoccasionto use. For example,you
may recallthat the sum of the first integersis We can indicatethis formulausingsigma
notation.The formulais givenhere alongwith two otherformulasthat will becomeusefulto us.

We can showfrom associative,commutative,and distributivelaws for real numbersthat

and

Example1:
Computethe followingquantityusingthe summationformulas:

Solution:

AnotherLookat Upperand LowerSums
We are now readyto formalizeour initialideasaboutupperand lowersums.

Let be a boundedfunctionin a closedinterval and the partitionof into
subintervals.