About This Chapter
How It Works:
- Find the lesson within this chapter that corresponds to what you're studying in the Fundamental Theorem of Calculus chapter of your textbook.
- Watch fun videos that cover the calculus principles 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.
You'll learn all of the calculus topics covered in the textbook chapter, including:
- Components of the fundamental theorem of calculus
- Ways to show antiderivatives using the fundamental theorem of calculus
- Steps involved in analyzing functions that are defined by integrals
- How the fundamental theorem of calculus is proved
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1. The Fundamental Theorem of Calculus
The fundamental theorem of calculus is one of the most important equations in math. In this lesson we start to explore what the ubiquitous FTOC means as we careen down the road at 30 mph.
2. Using the Fundamental Theorem of Calculus to Show Antiderivatives
In this lesson you will learn how the fundamental theorem of calculus allows us to represent definite integrals as antiderivatives. You'll then cement their relationship in your mind by working through an example problem.
3. Proving the Fundamental Theorem of Calculus
In this lesson we prove the two parts of the fundamental theorem of calculus by carefully explaining the anti-derivative and by cleverly defining and using some additional functions.
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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: Techniques of Antidifferentiation
- Saxon Calculus: Applications of Antidifferentiation
- Saxon Calculus: Numerical Approximation of Definite Integrals
- Saxon Calculus: Concept of Series
- Saxon Calculus: Series of Constants
- Saxon Calculus: Taylor Series