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Upper and Lower Riemann Sums

Upper and Lower Riemann Sums
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2013-07-13 00:36
FunctionCalculusIntegralGeometric Construction
In collections Calculus 1 Graphical Illustrations
This example demonstrates how upper and lower Riemann sums approximate definite integrals of a function. Key math concepts include Riemann sums, definite integrals, and function approximation. It is constructed using GeoGebra commands like Textfield, LowerSum, UpperSum, Integral, involving objects such as function f, input boxes a, b, n, and sliders for animation. Suitable for high school students and beginners in calculus learning integral concepts.

GeoGebra Commands & Parameters

  1. Textfield(f) → inputBox1
  2. Textfield(a) → inputBox2
  3. Textfield(b) → inputBox3
  4. LowerSum(f, a, b, n) → c
  5. UpperSum(f, a, b, n) → d
  6. Integral(f, a, b) → A

AI Drawing Prompt Reference

Draw a function graph and display its upper and lower Riemann sums to approximate the definite integral, with input boxes for the function, lower and upper limits, and a slider to adjust the number of partitions, while labeling the value of the definite integral to show how the upper and lower Riemann sums approximate the area under the function.
The prompt above was compiled from the original drawing commands and is for reference only.