Education Technology

### Mathematics lessons for IB® Diploma Programme

Analysis and Approaches | Calculus

# 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 subsequent 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.