Activity Overview
This activity is an application of integration. Students first use the calculator to determine specific numeric results to enable them to understand the dynamics of the problem.
Before the Activity
Students then use the symbolic capacity of their calculator and derivatives to find the maximum volume. This activity emphasizes using the integral of a rate of change to give the accumulated change. The definite integral of the rate of change of a quantity is interpreted as the change of the quantity.
See the attached Activity PDF file(s) for detailed instructions for this activity.
During the Activity
Follow the procedures outlined in the activity.
Students will:
Be able to use the calculator to determine specific numeric results in the context of the problem.
Be able to use the symbolic capacity of their calculator and derivatives to find the maximum volume.
Be able to use the integral of a rate of change to give the accumulated change.
Recognize that the definite integral of the rate of change of a quantity is interpreted as the change of the quantity.
After the Activity
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary