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The Area Between

Activity Overview

Students will find the area between two curves while determining the required amount of concrete needed for a winding pathway and stepping stones.

Key Steps

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    In problem 1, students use a scenario to help them explore the area between two curves. Students are to graph the functions and then use the Integral, Text, and Calculate tools to find the volume of the pathway.

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    In problem 2, the business owners decide to change the design of the pathway. Students are to model the two equations and graph them to find the amount of concrete needed.

    Students will see that when doing this by hand, the variable portion cancels itself out and they are integrating a constant.

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    In problem 3, students will find the volume of one stepping-stone. They graph the functions, find the intersection points using the Intersection Point(s) tool, and then find the volume of the stepping-stone.

    Students may think that f2 is the top function, but f1 is the top function in the interval.

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