About This Chapter
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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?
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.
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.
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Other chapters within the Calculus: Help and Review course
- Graphing and Functions: Help and Review
- Continuity in Calculus: Help and Review
- Geometry and Trigonometry in Calculus: Help and Review
- Using Scientific Calculators in Calculus: Help and Review
- Limits in Calculus: Help and Review
- Rate of Change in Calculus: Help and Review
- Calculating Derivatives and Derivative Rules: Help and Review
- Graphing Derivatives and L'Hopital's Rule: Help and Review
- Applications of Derivatives: Help and Review
- Area Under the Curve and Integrals: Help and Review
- Integration and Integration Techniques: Help and Review
- Differential Equations: Help and Review