This activity builds student comprehension of functions defined by a definite integral, where the independent variable is an upper limit of integration.
Students will compare constant and non-constant integrands.
First, students will examine a constant integrand.
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.
In problem 2, students investigate the behavior of a non-constant integrand.
They will see that the function changes at a non-constant rate.
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