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.
|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
To overestimate or underestimate? In this lesson, you will draw Riemann rectangles so the right side, left side or middle of the rectangle hits the curve.
2. How to Use Riemann Sums to Calculate Integrals
As a new property owner, you might relish mowing your lawn. Up and down your property you mow and measure out small sections to find the area of your property. In this lesson, you will discover what a Riemann sum approach is and how to calculate an estimated area using multiple slices.
3. 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.
4. Average Value Theorem
If you know you've gone 120 miles in 2 hours, you're averaging 60 mph. But what if you know your velocity at every point in time and not how far you've gone? In this lesson, learn how to calculate average values using integrals.
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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