Area under graph and Total Area of n Rectangles

Area under graph and Total Area of n Rectangles
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2016-02-01 15:27
This example demonstrates approximating the area under a function's graph using n rectangles, comparing it with the actual integral value. Core math concepts include definite integrals, Riemann sums (upper and lower), limit concepts, derivatives, and continuity. It uses GeoGebra commands/objects like Point, UpperSum, Integral, LowerSum, Textfield for visualization and explanation, suitable for high school and above learning calculus, numerical integration, and limits.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. UpperSum(f, x(A), x(B), n) → b
  4. Integral(f, 1, 2) → c
  5. LowerSum(f, x(A), x(B), n) → a
  6. Textfield(n) → InputBox1