3.2 Numerical Integration

In this lesson, you will learn about numerical integration.

Lesson Objectives

• • Review the definition of a definite integral as a limit of Riemann Sums.

  • Use appropriate technology to numerically estimate definite integrals using the midpoint, trapezoidal, and Simpson's rules.

  • Estimate errors involved in numeric integration.

Lesson Content

View all of the following instructional videos. These will help you master the objectives for this module.

• 1. YouTube video: 4.4 Riemann Sum and the Definite Integral

• 1. YouTube videos: Calculating a Definite Integral Using Riemann Sums and Rectangles when there is a "nice" formula available

  2. Part 1:

• 1. Part 2:

• 1. YouTube video: Trapezoidal Rule for Approximating Integrals

• 1. YouTube video: Simpson's Rule for Approximate Integrals

• 1. YouTube video: Simpon's rule: Error bound

Lesson Readings

The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.

• 1. The Definite Integrals - area as a limit of Riemann Sum, definition of definite integral, approximation of the definite integral: the midpoint rule, properties of definite integral, the Fundamental Theorem of Calculus, practice problems with answers

  2. Chapter 5: Definite Integral - Part 1: Numerical Integration- Riemann Sums, trapezoidal rule, mid-point rule, tangent line approximation, Simpson's rule, the definite integral as a limit of Riemann Sums

  3. Riemann Sums and the Definite Integral- Riemann sums, converting Riemann sums to definite integrals, how to evaluate a definite integral, properties of definite integrals, average value of an arbitrary continuous function

  4. Numerical Integration- the trapezoidal rule, Simpson's rule

  5. Chapter 8: Numerical Integration- integration, numerical integration, midpoint rule, trapezoidal rule, Simpson's rule, error estimates

Lesson Practice Exercises/Activities

Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.

6.3: The Definite Integral: Numerical and Graphical Approaches

Additional Resources

Below are additional resources that help reinforce the content for this module.

• 1. YouTube video: Lecture 24: Numerical Integration

• 1. Riemann Sum and Definite Integrals for AP Calculus

  2. Riemann Sums

1. 4.3 Riemann Sums and Definite Integrals

   1. Numerical Integration

   2. Numerical Integration