Activities

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?

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 are under the curve.

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.