In this activity, students will look at the graph of a function g, defined to be the integral of a function f, with the goal of understanding Part 1 of the Fundamental Theorem of Calculus. Specifically, students will see that g is related to the area under the graph of f from a to x. They will also notice that the graph of g is the antiderivative of f, thereby providing graphical support for Part 1 of the Fundamental Theorem of Calculus.
Before the Activity
Download the attached PDF and look over the information on the first page. Download and distribute the attached .tns file and Student Worksheet for use during the activity.
During the Activity
Discuss the material from the activity pages and worksheet with students as needed.
After the Activity
Encourage students to summarize what they have learned from completing the activity.