Education Technology

Exploring the Area Under a Curve

Activity Overview

Students explore Riemann sums to find the approximate area under the graph of a parabola on the interval [0, 1].

Key Steps

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    Students focus on two questions that define the activity:

    How can you use rectangles to approximate the area under the curve y=y 2 and above the x-axis.

    Is there a way to use rectangles to find the exact area under the curve?

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    Students make use of five right-endpoint rectangles to find an approximation of the area under the curve.

    Students will be introduced to the Riemann sum. They explore the Riemann sum with right-endpoints.

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    Next, students use five left-endpoint rectangles to find an approximation of the are under the curve.

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    Finally, students summarize their findings. They will notice that the concavity of a function and whether it is increasing or decreasing will determine which estimates are overestimates verses underestimates.