Education Technology

Introduction to the Fundamental Theorem

Activity Overview

This activity builds student comprehension of functions defined by a definite integral, where the independent variable is an upper limit of integration.

Key Steps

  • Image

    Students will compare constant and non-constant integrands.

    First, students will examine a constant integrand.

  • Image

    Students will notice that there is a constant rate of change, of 1.5, in the graph of f (x) = 1.5.

    They will record the outputs and create a scatter plot of the ordered pairs. They will see that the graph is a line with a slope of the constant.

  • Image

    In problem 2, students investigate the behavior of a non-constant integrand.

    They will see that the function changes at a non-constant rate.