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.
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- Complete the quiz after watching each video lesson to test your understanding.
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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
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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 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