Integration

Abstract

In Chapter 4 the Riemann integral of a function f on an interval I was defined as follows: Partition the interval I into small intervals I _k. In each I _k choose a point ξ _k Define the integral to be the limit of the sums

$$\sum\limits_{k = 1}^n {\int {\left( {{\xi _k}} \right)} } \iota \left( {{I_k}} \right)$$

where l(I _k ) is the length of I _k , and the limit is taken as the maximum length goes to 0.