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Four Riemann Sum Methods Comparison

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About This MicroSim

This comprehensive visualization compares all four Riemann sum approximation methods:

  • Left: Uses left endpoint of each subinterval
  • Right: Uses right endpoint of each subinterval
  • Midpoint: Uses midpoint of each subinterval
  • Trapezoidal: Averages left and right (connects with straight lines)

The comparison table highlights which method gives the best approximation.

Iframe Code

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<iframe src="https://dmccreary.github.io/calculus/sims/riemann-sum-methods/main.html" height="602px" scrolling="no" style="width: 100%;"></iframe>

Lesson Plan

Learning Objectives

Students will be able to:

  1. Compare the accuracy of different Riemann sum methods
  2. Evaluate which method provides the best approximation for a given function
  3. Explain why midpoint and trapezoidal methods are often more accurate

Activities

  1. Method Exploration (5 min): Select each method and observe how rectangles/trapezoids differ
  2. Error Analysis (10 min): For each function, identify which method has the smallest error
  3. Pattern Discovery (5 min): Why do midpoint and trapezoidal methods tend to be more accurate?

Key Insights

  • Midpoint and trapezoidal methods typically have smaller errors
  • The trapezoidal rule is the average of left and right sums: \(T_n = \frac{L_n + R_n}{2}\)
  • Error decreases as n increases for all methods

References