Education Technology

Calculus: Trapezoid and Midpoint Rules

by Texas Instruments


  • Identify whether rectangle or trapezoidal approximations will provide an overestimate or an underestimate of the area under a curve from a positive function graph
  • Order the estimates of area under a curve
  • Describe the relationship of concavity to the midpoint and trapezoidal approximations


  • trapezoidal approximations
  • left, right, and midpoint rectangle approximations
  • area under a curve

About the Lesson

This lesson involves providing students with a visual representation of area estimation methods in order to determine which is most accurate. As a result, students will:

  • Observe the left endpoint rectangle, right endpoint rectangle, and trapezoidal estimates of the area under the curve in order to observe and make predictions about the accuracy of each estimate.
  • Experience a dynamic comparison of the midpoint rectangle and trapezoidal estimates of area under a curve, relating these to the concavity of the curve.
  • Suggest their own geometric estimation methods for area under a curve to improve on the accuracy of the midpoint rectangle estimate.