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.


  • 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.


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

About the Lesson

This activity is done mainly by hand, but uses the TI-84 family as an aid to the problems.