About This Chapter
Who's it for?
This unit of our AP Calculus Homeschool course will benefit any student who is trying to learn about integration applications. There is no faster or easier way to learn about calculus. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn to find location as a function of time.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a calculus curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and an Integration Applications unit exam confirm understanding or identify any topics that require review.
Integration Applications Unit Objectives:
- Learn to calculate volumes using single integrals.
- Find volumes of revolution with integration.
- Calculate enclosed areas using root finding and integration.
- Learn to use integration in motion.
1. Integration and Dynamic Motion
This lesson uses driving to demonstrate how graphing can help you use calculus to figure out how fast you were going at a given time. Using this lesson, you can learn how to integrate your velocity to find your position.
2. How to Find Simple Areas With Root Finding and Integration
Combine your calculus tools in this lesson! Find the area enclosed by multiple arbitrary functions by first finding the root of an equation and then integrating over the resulting range.
3. How to Find Area Between Functions With Integration
Sometimes you aren't looking for the area under the curve; after all, not every region is between a curve and axis! In this lesson, learn how to find areas between curves as well as areas with complicated boundaries.
4. How to Calculate Volumes Using Single Integrals
Ever wonder where the equation for the volume of a cone comes from? Or the equation for the volume of a sphere? In this lesson, learn how to use a slicing technique to find the volume of a region by solving a single integral.
5. How to Find Volumes of Revolution With Integration
Some shapes look the same as you rotate them, like the body of a football. In this lesson, learn how to find the volumes of shapes that have symmetry around an axis using the volume of revolution integration technique.
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Other chapters within the AP Calculus AB & BC: Homeschool Curriculum course
- Functions - AP Calculus: Homeschool Curriculum
- Graphing & Functions - AP Calculus: Homeschool Curriculum
- Sequences & Series - AP Calculus: Homeschool Curriculum
- Limits - AP Calculus: Homeschool Curriculum
- Continuity - AP Calculus: Homeschool Curriculum
- Exponentials & Logarithms: Homeschool Curriculum
- Exponents & Polynomials - AP Calculus: Homeschool Curriculum
- Applications of Derivatives - AP Calculus: Homeschool Curriculum
- Calculating Derivatives & Derivative Rules - AP Calculus: Homeschool Curriculum
- Differential Equations - AP Calculus: Homeschool Curriculum
- Area Under the Curve & Integrals - AP Calculus: Homeschool Curriculum
- Graphing Derivatives & L'Hopital's Rule - AP Calculus: Homeschool Curriculum
- Integration & Integration Techniques - AP Calculus: Homeschool Curriculum
- Rate of Change - AP Calculus: Homeschool Curriculum
- Geometry and Trigonometry - AP Calculus: Homeschool Curriculum
- Using Scientific Calculators - AP Calculus: Homeschool Curriculum