Roman C. answered • 05/26/16

Tutor

4.9
(637)
Masters of Education Graduate with Mathematics Expertise

A Riemann Sum for ∫

_{a}^{b}f(x) dx is when you chop up the interval [a,b] into n subintervals [a_{i},a_{i+1}] where a = a_{0}< a_{1}< ... < a_{n}= b and pick an x_{i}in each interval. You get rectangles of width a_{i+1}- a_{i}and height f(x_{i}). The sum of their areas approximates the integral.To get the exact value of the integral from the Riemann Sum, you take the limit as follows:

1. n → ∞ (Large number of subintervals).

2. max

_{i=1,...n}(a_{i+1}- a_{i}) → 0 (All subintervals have small length).This method of computing the integral is called Riemann Integration, and is used as the definition for Integration in Calculus 1 and 2, since it is sufficient for integrals of continuous functions to be well defined.