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Activity Overview

In this activity, students will build on their comprehension of functions defined by a definite integral, where the independent variable is an upper limit of integration. Students are led to the brink of a discovery of a discovery of the Fundamental Theorem of Calculus.

Key Steps

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    Students will compare constant and non-constant integrands. First, students will examine a constant integrand.

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    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.

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    In problem 2, students investigate the behavior of a non-constant integrand. They will see that the function changes at a non-constant rate.