# Activities

• • • ##### Subject Area

• Math: Calculus: Applications of Integral, Antiderivatives and Definite Integrals

• ##### Author 9-12

45 Minutes

• ##### Device
• TI-Nspire™
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

## Riemann's Sums: Using the area of rectangles to approximate the integral of a function from a to b

#### Activity Overview

Students will use the graph of a function to draw rectangles over the interval [a,b] and measure their area. As the numbers of rectanges increase they will see the approximate area become more accurate. In the last step, they will use the TI-Nspire to measure the intergral over the same interval [a,b] and make the connection.

#### Before the Activity

Download the needed TNS file and send to students' calculators. Make copies of handout as needed.

#### During the Activity

Once the student opens the document, the student will begin with creating one rectangle over [a,b] and find the area of it. Then on the student worksheet, record the area and discuss whether that is a good approximation.
From there the teacher will discuss what will happen with two rectangles. Then the student will draw two rectangles, find the area of each one, and add them together. Then the class will repeat this cycle with 5, and 10 rectangles. When they have finished all of the rectangle areas, the last step will be for the class to use the measurement option to find the integral of the function over [a,b] and compare the rectangle method to the actual integral.

#### After the Activity

The teacher could use this activity as an introduction to the definition of Riemann Sums and expand on it with other approximation methods. Maybe repeat it with trapezoids and use a smaller width.