# Ch 27: Saxon Calculus: Numerical Approximation of Definite Integrals

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Numerical Approximation of Definite Integrals chapter of your textbook.
- Watch fun videos that cover the calculus concepts you need to learn or review.
- Complete the quiz after watching each video lesson to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material, or submit a question for one of our instructors.

## Chapter Topics

You'll learn all of the calculus topics covered in the textbook chapter, including:

- Calculating definite integrals using Riemann Sums
- Explanation of the trapezoid rule
- Approximating definite integrals using technology
- How to approximate definite integrals with Taylor series

*Saxon is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. Using Riemann Sums to Calculate Definite Integrals

Riemann sums provide a way to calculate definite integrals. The definite integral represents the area under a function, and has a wide variety of applications in math and science.

### 2. What is the Trapezoid Rule?

In this lesson, you'll move beyond simple rectangles to estimate the area under a curve. Get more sophisticated with your approximations and use trapezoids instead of those pesky rectangles.

### 3. Using Taylor Series to Approximate Definite Integrals

In this lesson, we explore how to approximate definite integrals using the Taylor series. Using a simple example at first, we then move on to a more complicated integral where the Taylor series approach is very effective.

### 4. Using Technology to Approximate Definite Integrals

At times, solving for definite integrals by hand may prove to be too tedious of a process. In this event, use of a scientific calculator, specifically the Texas Instruments TI-83 or 84, can make this process much easier.

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### Other Chapters

Other chapters within the Saxon Calculus Homeschool: Online Textbook Help course

- Saxon Calculus: Real Numbers
- Saxon Calculus: Algebra
- Saxon Calculus: Algebra Theorems
- Saxon Calculus: Geometry
- Saxon Calculus: Logic
- Saxon Calculus: Trigonometry
- Saxon Calculus: Graphing Calculator
- Saxon Calculus: Basics of Functions
- Saxon Calculus: Graphing Functions & Equations
- Saxon Calculus: Analysis of Graphs
- Saxon Calculus: Limits of Functions
- Saxon Calculus: Asymptotic & Unbounded Behavior
- Saxon Calculus: Continuity as a Property of Functions
- Saxon Calculus: Parametric, Polar & Vector Functions
- Saxon Calculus: Concept of the Derivative
- Saxon Calculus: Derivative at a Point
- Saxon Calculus: Derivative as a Function
- Saxon Calculus: Second Derivatives
- Saxon Calculus: Applications of the Derivative
- Saxon Calculus: Computation of Derivatives
- Saxon Calculus: Riemann Sums
- Saxon Calculus: Interpretations & Properties of Definite Integrals
- Saxon Calculus: Applications of Integrals
- Saxon Calculus: Fundamental Theorem of Calculus
- Saxon Calculus: Techniques of Antidifferentiation
- Saxon Calculus: Applications of Antidifferentiation
- Saxon Calculus: Concept of Series
- Saxon Calculus: Series of Constants
- Saxon Calculus: Taylor Series