Lecture 16 : Integral from upper and lower sums [Section 16.1]
is called the length of the subinterval .
(iv)
For a partition , the number
is called the norm of the partition .
Assumptions: In order to define the area bounded by the graph of a function , the and the lines , we assume that is a continuous function. As a consequence of this property not only is bounded on every closed subinterval of in fact it attains its bounds in that interval.
16.1.2
Definition:
Let be a continuous function and let
be a partition of .
. 
, the number 
. 
, the 
and the lines 
, we assume that 
is a continuous function. As a consequence of this property not only 
is bounded on every closed subinterval of 
in fact it attains its bounds in that interval. 
be a continuous function and let 
. 
