About This Chapter
Below is a sample breakdown of the Integration Applications chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.
|Day||Topics||Key Terms and Concepts Covered|
|Monday||Integration and Dynamic Motion||The process of solving dynamic motion|
|Tuesday||How to Find Simple Areas with Root Finding and Integration||Calculating areas and separating integrals into two parts|
|Wednesday||How to Find Area Between Functions with Integration||Methods for calculating total areas|
|Thursday||How to Calculate Volumes Using Single Integrals||A look at how to estimate a cone's volume|
|Friday||How to Find Volumes of Revolution with Integration||Techniques for finding the volume of symmetrical shapes|
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 Calculus Syllabus Resource & Lesson Plans course
- Graphing & Functions: Calculus Lesson Plans
- Continuity: Calculus Lesson Plans
- Geometry & Trigonometry: Calculus Lesson Plans
- Using Scientific Calculators: Calculus Lesson Plans
- Limits: Calculus Lesson Plans
- Rate of Change: Calculus Lesson Plans
- Calculating Derivatives: Calculus Lesson Plans
- Derivative Graphs & L'Hopital's Rule: Calculus Lesson Plans
- Applications of Derivatives: Calculus Lesson Plans
- Area Under the Curve & Integrals: Calculus Lesson Plans
- Integration: Calculus Lesson Plans
- Differential Equations: Calculus Lesson Plans