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