The document provides an introduction to Riemann sums, detailing their use in calculus to estimate the area under curves and define integrals. It discusses left and right Riemann sums with examples and includes a sample question on calculating a left Riemann sum for a specific function. Additionally, it covers the use of sigma notation for managing large summations.

1. Introduction to
Riemann sums
Daniel Xu
First Year Calculus

2. Sums
01
Left Riemann
Sum
Integration
definition
02
03 Sample Question
04
TABLE OF CONTENTS

3. Sums
When calculating large sums,
we can use Σ notation to
denote large sums as opposed
to writing it all out.

4. Summation examples

5. What is an integral?
An integral can be defined as
the area under a curve or
function, bounded by the x-
axis on an interval.

6. A basic integral
This can be computed as 5 × 2.
However, it can also be written
as

8. Midpoint
Examples of Riemann Sums
Left Right

9. The Riemann Sum

10. The Riemann Sum

11. The Left-hand
Riemann Sum

12. Sample Question
Find the Left Riemann sum of the function f(x)=x+7 on the interval [0,8] divided
into four sub-intervals.