Education Technology

Exploring the Area Under a Curve

Published on 11/29/2011

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 = x2 and above the x-axis?

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

    Students discuss the goal of the activity, which is to use rectangles to approximate the area under a 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 area under the curve.

    Students will see that the first rectangle has a height of zero and unlike the right-endpoint approximation a unit of measure shifts down each value of x.