Education Technology

# Activities

• ##### Subject Area

• Math: Calculus: Definite Integrals and Applications

9-12

45 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

4.0

## Riemann Sums

#### Activity Overview

Visualize values for different Riemann sums and use these values to estimate the area of a region.

#### Objectives

• Learn that for a continuous nonnegative function f, there is one interpretation of the definite integral f(x)dx from a to b, the area of the region R, bounded above by the graph of y = f(x), below by the x-axis, and by the lines x = a and x = b
• Visualize and compute values for three different Riemann sums: left-hand endpoint, right-hand endpoint, and midpoint, and use these values to estimate the area of a region R
• Learn about the nature of these estimates as the number of rectangles increases
• Consider other functions and relate these Riemann sums to function characteristics

#### Vocabulary

• Riemann sum
• Left-hand endpoint, right-hand endpoint, and midpoint sum
• Area of a plane region
• Underestimate, overestimate
• Definite integral
• Continuous