Lecture 16 : Integral as a limit of Riemann sums [Section 16.2]
16.2
Integral as a Limit of Riemann sums
Through theorem 16.1.7 allows us to check whether a function is integrable or not, it is not very convenient to find . For this, we consider another way of approximating the required area.
16.2.1
Definition:
Consider a function . Given any partition
of , for , choose arbitrarily and define the sum
The product is the area of the rectangle over the interval with height . The sum is called a Reimann sum of with respect to the partition and the choice of the points .
. For this, we consider another way of approximating the required area. 
. Given any partition 
, for 
, choose 
arbitrarily and define the sum 
is the area of the rectangle over the interval 
with height 
. The sum 
is called a 
with respect to the partition 
and the choice of the points 
. 
