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Ch 14: Integration Applications - AP Calculus: Homeschool Curriculum

About This Chapter

The Integration Applications unit of this AP Calculus Homeschool course is designed to help homeschooled students learn about integration applications. Parents can use the short videos to introduce topics, break up lessons and keep students engaged.

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.

5 Lessons in Chapter 14: Integration Applications - AP Calculus: Homeschool Curriculum
Test your knowledge with a 30-question chapter practice test
Integration and Dynamic 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.

How to Find Simple Areas With Root Finding and Integration

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.

How to Find Area Between Functions With Integration

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.

How to Calculate Volumes Using Single Integrals

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.

How to Find Volumes of Revolution With Integration

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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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