Education Technology

Bounded Areas

Subject Area
Math: Calculus: Definite Integrals and Applications
Math: IB: Analysis-Approaches
Math: IB: Applications-Interpretations
Math: AP Calculus: AP Calculus
Level
9-12
Activity Time
50 Minutes
Software
TI-Nspire™ CX
TI-Nspire™ CX CAS
TI Calculator
TI-Nspire™ CX series
TI-Nspire Version
5.0
Resource Types
Lessons
Exam Prep
Format
TNS

Bounded Areas

Activity Overview

In this lesson, students will compare the Riemann Sum area estimates with the exact bounded area of a curve and the x-axis. 

Objectives

  • Students will practice and discuss applications of finding the area bounded by a curve and the x-axis.
  • Students will apply this information to finding the area bounded by two curves.
  • Students will try to make a connection with how to understand these topics in both IB Mathematics and AP Calculus and on their final assessments.
 

Vocabulary

  • Riemann Sums         
  • Underestimate     
  • Overestimate
  • Definite Integrals       
  • Bounded Areas     
  • Concavity
 

About the Lesson

Students will use the pages of this TI-Nspire activity to refresh their skills on left-hand rectangle, right-hand rectangle, midpoint rectangle, and trapezoidal Riemann Sums given the bounded area between , the x-axis, and the vertical lines x = 1 and x = 3. For the remainder of this activity, we will call this bounded area .


 

Subject Area
Math: Calculus: Definite Integrals and Applications
Math: IB: Analysis-Approaches
Math: IB: Applications-Interpretations
Math: AP Calculus: AP Calculus
Level
9-12
Activity Time
50 Minutes
Software
TI-Nspire™ CX
TI-Nspire™ CX CAS
TI Calculator
TI-Nspire™ CX series
TI-Nspire Version
5.0
Resource Types
Lessons
Exam Prep
Format
TNS
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