Introduction
In the last section we discussed how to find the area of a closed interval using geometry and how to estimate it using rectangles. In this section we will expand our definition of a sum and how it relates to integrals. We will also use geometry to find the area under a curve.
Objective: We address topic 3 (pdf) in the AP course outline. By the end of thissection you will be able to use the area under a curve to evaluate a definite integral.
Topics in this section include:
- 5-2.1 - Riemann Sums - The Basics
- 5-2.2 - Riemann Sums - The Notation
- 5-2.3 - Riemann Sums - Errors to Avoid
- 5-2.4 - Evaluating an Integral with the Calculator
Guiding Question
As you navigate through this section, ask yourself the following question:
- Do you think we will be able to use accurately use geometric formulas to find the area under a curve with the majority of the functions we look at? If not, why not?
Now that you are familiar with the topics we will cover in this section of Module 5, you are ready to begin. Please click the menu item under Section called Riemann Sums - The Basics to begin 5-2.1 - Riemann Sums - The Basics.
Photo Attribution
Description: A hand using a TI-83 calculator against a white background
Source: iStock.com