About This Chapter
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.
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 Math 104: Calculus course
- Graphing and Functions
- Geometry and Trigonometry
- How to Use a Scientific Calculator
- Rate of Change
- Calculating Derivatives and Derivative Rules
- Graphing Derivatives and L'Hopital's Rule
- Applications of Derivatives
- Area Under the Curve and Integrals
- Integration and Integration Techniques
- Differential Equations
- Studying for Math 104