# Ch 18: Approximating Definite Integrals

### About This Chapter

## Approximating Definite Integrals - Chapter Summary and Learning Objectives

The definite integral of a function is important for many applications which utilize calculus. These can be found in a number of fields, most notably the sciences and engineering. The definite integral is similar to the antiderivative and indefinite integral of a function. The main difference is that the definite integral is a real number value, while antiderivative and indefinite integral values represent an infinite number of functions differing by a single constant. You'll begin to understand more about definite integrals in these lessons. in them, you'll learn things like:

- How to identify Riemann sums
- The process of drawing left, right and middle Riemann sums
- How to understand the linear properties of definite integrals
- What the average value theorem is and how it works

The lessons in this chapter give you practice questions and quizzes that can test your comprehension of the topics. Each component is divided into manageable video lessons to help you understand the fundamental elements of approximating definite integrals.

Video | Objective |
---|---|

How to Identify and Draw Left, Right and Middle Riemann Sums | Learn techniques for identifying and drawing different types of sums. |

What is the Trapezoid Rule? | Define the trapezoid rule and study its benefits. |

Linear Properties of Definite Integrals | Analyze the linear properties of definite integrals. |

Average Value Theorem | Gain experience using the average value theorem. |

### 1. How to Identify and Draw Left, Right and Middle Riemann Sums

The Riemann sum is the area between f(x) and the x-axis and it's given by the sum over k=1 to k=n of f(x sub k). Learn more about this mathematical equation, the formula's methodology, and how to draw left, right, and middle Riemann sums.

### 2. How to Use Riemann Sums to Calculate Integrals

Riemann sums use the method of 'slicing' the area of a graph to isolate the equation used to calculate definite integrals. Follow example problems of using Riemann sums to find an area even when divided into different sections.

### 3. What is the Trapezoid Rule?

The trapezoid rule is a way to find the area underneath a curve, using trapezoids to estimate the area, rather than rectangles. Learn more about the trapezoid rule and using trapezoids tot estimate area. Also, review Riemann sum in this lesson.

### 4. Average Value Theorem

The calculation of the average values of equations using integrals can be done using the average value theorem. Learn more about the average value theorem, how to display it on graphs, and how to calculate continuous functions.

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### Other Chapters

Other chapters within the AP Calculus AB: Exam Prep course

- Graph Basics
- The Basics of Functions
- How to Graph Functions
- Limits of Functions
- Continuity of Functions
- Understanding Exponentials & Logarithms
- Using Exponents and Polynomials
- Properties of Derivatives
- The Derivative at a Point
- The Derivative as a Function
- Second Derivatives
- Using Derivatives
- Computing Derivatives
- Properties of Definite Integrals
- Applications of Integrals
- Using the Fundamental Theorem of Calculus
- Understanding & Applying Integration Techniques
- Using a Scientific Calculator for Calculus
- About the AP Calculus Exam
- AP Calculus AB Flashcards