Additional Resources
OpenStax Online Textbook
How to Read a Math Textbook
Additional Instructional Resources
Net Change Theorem- FTC6
Objectives
- Explain the significance of the Net Change Theorem
- Use the Net Change Theorem to solve applied problems
Summary
The net change theorem considers the integral of a rate of change. The net change theorem states that the integral of a rate of change will describe the net change between the given limits.
In essence, if we had a function describing the rate of change of a container filling up, , with limits and describing time, then the amount of liquid put into the container between time and time can be found by doing the following
In the setting where we consider the integral of a velocity function , measures the exact change in position of the moving object on when [,]; when is nonnegative, is the object's distance traveled on [,].