Ch 12: Integration Applications

About This Chapter

Watch integration applications video lessons with accompanying quizzes for immediate feedback. Learn differential notation, proportional population dynamics and more.

Integration Applications

Once you've learned about integration and integration techniques, it's time to move on to applications. Not to be confused with integration application used in software development and engineering, these calculus functions are important and often used in everyday life. These are just a few of the integral applications that come up in the calculus field. Don't be surprised to see many more appear as you continue your lessons.

Throughout these lessons, you'll be introduced to these integration applications. Watch each application and equation explained and then proven with examples. Our instructors teach these lessons with multiple examples to provide the clearest understanding of functions, methods and applications. If you have trouble following the video, read along with the text. Then take the short quiz following each lesson to assess your understanding. Unlike live lectures, these lessons allow you to re-watch any topic or problem that you may need clarification on.

During these lessons, study Newton's method for root-finding problems and other root-finding solutions. Next, learn how to find location (using a function of time) and areas between functions. Finally, learn how to calculate volumes. Discover how to find volumes of revolution for all shapes with curved edges, including disks and cylinders. Also, discover how to find volumes using single integrals.

5 Lessons in Chapter 12: Integration Applications
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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