Ch 12: Integration Applications: Help and Review

About This Chapter

The Integration Applications chapter of this College Calculus Help and Review course is the simplest way to master integration applications. This chapter uses simple and fun videos that are about five minutes long, plus lesson quizzes and a chapter exam to ensure you learn the essentials of integration calculations.

Who's it for?

Anyone who needs help understanding integration applications will benefit from taking this course. You will be able to grasp the subject matter faster, retain critical knowledge longer and earn better grades. You're in the right place if you:

  • Have fallen behind in understanding integration applications or finding volumes.
  • Need an efficient way to learn about integration applications.
  • Learn best with engaging auditory and visual tools.
  • Struggle with learning disabilities or learning differences, including autism and ADHD.
  • Experience difficulty understanding your teachers.
  • Missed class time and need to catch up.
  • Can't access extra math learning resources at school.

How it works:

  • Start at the beginning, or identify the topics that you need help with.
  • Watch and learn from fun videos, reviewing as needed.
  • Refer to the video transcripts to reinforce your learning.
  • Test your understanding of each lesson with short quizzes.
  • Submit questions to one of our instructors for personalized support if you need extra help.
  • Verify you're ready by completing the Integration Applications chapter exam.

Why it works:

  • Study Efficiently: Skip what you know, review what you don't.
  • Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
  • Be Ready on Test Day: Use the Integration Applications chapter exam to be prepared.
  • Get Extra Support: Ask our subject-matter experts any relevant question. They're here to help!
  • Study With Flexibility: Watch videos on any web-ready device.

Students will review:

In this chapter, you'll learn the answers to questions including:

  • How can I incorporate velocity to determine my position?
  • How can I use integration and root finding to calculate simple areas?
  • How can I use integration to calculate the area between functions?
  • How can I compute volume with single integrals?
  • How can I use integration to calculate volumes of revolution?

6 Lessons in Chapter 12: Integration Applications: Help and Review
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.

Integrating Factor: Method & Example

6. Integrating Factor: Method & Example

,It's nice to get solutions to differential equations. When faced with a first-order linear differential equation we can use the integrating factor method to get a solution. In this lesson, we'll use examples to explain this method.

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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