This lesson on using Riemann sums to find the area under the graph of a function is intended for students enrolled in AP Calculus AB or BC, Calculus Honors, or College Calculus.
The procedure outlined in this e-book is a step by step example on how one can approximate the net area between the x-axis and the curve y=f(x) for a ≤ x ≤ b using Riemann Sums. Given any continuous function f(x), and the values a, b and n, the number of subintervals, it is possible to approximate the area under the curve of f(x).
By using the concept of limits at infinity, it is possible to extend the idea to compute the exact area under the curve of f(x). This example can be duplicated for different continuous functions over [a,b].
This document is an excellent one for calculus students in high school and college students. Instructors will also benefit from the outline.