About This Chapter
How It Works:
- Find the lesson within this chapter that corresponds to what you're studying in the Techniques of Antidifferentiation chapter of your textbook.
- Watch fun videos that cover the calculus you need to learn or review.
- 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:
- Explanation of antiderivatives and integrals
- Antiderivatives of products and constants
- Antidifferentiating sums and logarithmic functions
- Computing integrals of exponential and trigonometric functions
- Using substitution to solve integrals and working with trig substitution
- Integrating functions with partial fractions, factorizing functions
- How to use integration by parts and solve improper integrals
- Understanding piecewise integration and changing limits of definite integrals
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1. Indefinite Integrals as Anti Derivatives
What does an anti-derivative have to do with a derivative? Is a definite integral a self-confident version of an indefinite integral? Learn how to define these in this lesson.
2. Antiderivatives of Constants & Power Functions
In the study of calculus, you are frequently called on to find the antiderivative of a function. In this lesson, you'll learn how to find antiderivatives of constants and power functions.
3. Antiderivatives of Products of Constants & Functions
Antiderivatives are an undoing of a derivative in a way. This lesson will review what an antiderivative is and will then go on to explain a particular rule that tells us how to find the antiderivative of the product of a constant and a function.
4. How to Antidifferentiate Sums
In this lesson, we'll review antiderivatives then explore how to antidifferentiate sums of functions using a formula for the antiderivative of a sum. We'll apply the formula to multiple examples to help solidify our understanding of the concept.
5. How to Calculate Integrals of Exponential Functions
Exponential functions are so predictable. It doesn't matter how many times you differentiate e^x, it always stays the same. In this lesson, learn what this means for finding the integrals of such boring functions!
6. How to Antidifferentiate Logarithmic Functions
In this lesson, we demonstrate how to evaluate four types of integrals involving a logarithmic function. The method we use for each is Integration by Parts, and one of the key tricks is realizing a constant function is the derivative of a linear function. The natural logarithm works well with this since its derivative is 1/x.
7. How to Calculate Integrals of Trigonometric Functions
Ever feel like you are going around in circles? Like, periodically you have your ups and downs? Well, sines and cosines go up and down regularly too. In this lesson, learn how to integrate these circular functions.
8. How to Solve Integrals Using Substitution
Some integrals are as easy as riding a bike. But more often, integrals can look like deformed bikes from Mars in the year 3000. In this lesson, you will learn how to transform these scary-looking integrals into simpler ones that really are as easy as riding a bike.
9. How to Change Limits of Definite Integrals
In this lesson, we will discuss changing the limits of definite integrals. This is useful when using u-substitution or trigonometric substitution to solve definite integrals and saves time as there is no need to revert back to the original variable.
10. Using Integration By Parts
Your mother may have warned you not to bite off more than you can chew. The same thing is true with integration. In this lesson, learn how integration by parts can help you split a big interval into bite-sized pieces!
11. Partial Fractions: How to Factorize Fractions with Quadratic Denominators
Adding fractions with different denominators is something you probably learned how to do in algebra. In this lesson, learn how to do the opposite: take a complicated fraction and turn it into two simpler ones.
12. How to Integrate Functions With Partial Fractions
In this lesson, learn how to integrate complicated fractions by using the partial fractions technique. That is, you will turn a complicated fraction into something a bit easier to integrate by finding partial fractions!
13. Understanding Trigonometric Substitution
Sometimes a simple substitution can make life a lot easier. Imagine how nice it would be if you could replace your federal tax form with a 'Hello, my name is...' name badge! In this lesson, we review how you can use trigonometry to make substitutions to simplify integrals.
14. How to Solve Improper Integrals
What does it mean when an integral has limits at infinity? These integrals are 'improper!' In this lesson, learn how to treat infinity as we study the so-called improper integrals.
15. Piecewise Integration: Definition & Examples
Integration is finding the area between a function and the x-axis. Piecewise functions have separate expressions based on x-axis conditions. In this lesson, we'll learn how to integrate piecewise 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: Fundamental Theorem of Calculus
- 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