Module 7: Applications of Integration
Now that you can compute integrals, it is time to apply them! This module covers area between curves, volumes of solids of revolution using disk/washer and shell methods, and the average value of a function.
Your Progress
Learning Objectives
By the end of this module, you will be able to:
- Compute the area between two curves
- Find volumes of solids of revolution using disk and washer methods
- Apply the shell method for cylindrical shells
- Calculate the average value of a function on an interval
Module Lessons
Area Between Curves
Set up and evaluate integrals that compute the area enclosed between two curves. Learn to identify which function is on top and when to integrate with respect to y.
40-50 minutes
Volumes: Disk and Washer Methods
Compute volumes of solids formed by revolving a region around an axis using the disk and washer methods.
45-55 minutes
Volumes: Shell Method
Use cylindrical shells to find volumes of revolution, especially when the disk/washer method is inconvenient.
40-50 minutes
Average Value of a Function
Define and compute the average value of a continuous function and apply the Mean Value Theorem for Integrals.
30-40 minutes