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Mathematics lessons for IB® Diploma Programme

Applications and Interpretation | 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

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.