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Left Rectangle Approximation for Area Under a Curve

Left Rectangle Approximation for Area Under a Curve
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2019-01-22 12:12
FunctionCalculusIntegral
This example demonstrates the left rectangle approximation method for estimating the area under a curve. Key mathematical concepts include integration, rectangle area calculation, and function graphs. Using GeoGebra commands such as Sequence, Sum, NIntegral, and Segment, a series of rectangles are constructed to approximate the area under the curve. Suitable for high school mathematics education and learning integration concepts.

GeoGebra Commands & Parameters

  1. Sequence(Polygon[(2 + (i * Dx), 0), (2 + ((i + 1) * Dx), 0), (2 + ((i + 1) * Dx), f(2 + (i * Dx))), (2 + (i * Dx), f(2 + (i * Dx)))], i, 0, n - 1) → l3
  2. Sequence(Area[Polygon[(2 + (i * Dx), 0), (2 + ((i + 1) * Dx), 0), (2 + ((i + 1) * Dx), f(2 + (i * Dx))), (2 + (i * Dx), f(2 + (i * Dx)))]], i, 0, n - 1) → A
  3. Sum(A) → Rectangles
  4. NIntegral(f, 2, 5) → Area
  5. Segment((2 + (4 * Dx), -0.25), (2 + (5 * Dx), -0.25)) → g
  6. Segment((2 + (4 * Dx) + (0.2 * Dx), 0), (2 + (4.2 * Dx), f(2 + (4 * Dx)))) → h