MathPlotAI Logo MathPlotAI

Integral Estimated by Rectangles

Integral Estimated by Rectangles
Loading the math board and drawing, please wait…
2015-06-30 10:21
FunctionCalculusIntegralGeometric ConstructionSlider Animation
This example demonstrates how to estimate the area under a function curve using the rectangle method. It involves core mathematical concepts like definite integrals, rectangular approximation, and geometric interpretation. Constructed with GeoGebra commands such as Textfield, Point, Sequence, Take, and IntegralBetween to create functions, points, sequences, and integration intervals, along with rectangles. Suitable for high school calculus instruction to visually understand the geometric meaning and approximation methods of integrals.

GeoGebra Commands & Parameters

  1. Textfield(f) → inputBox1
  2. Point(xAxis) → A
  3. Point(xAxis) → B
  4. Sequence(x(A) + (i * dx), i, 0, n) → subint
  5. Take(subint, 1, n) → left
  6. Take(subint, 2, n + 1) → right
  7. Sequence(Polygon[(Element[left, i], 0), (Element[right, i], 0), (Element[right, i], Element[rightheights, i]), (Element[left, i], Element[rightheights, i])], i, 1, n) → rightRect
  8. Sequence(Polygon[(Element[left, i], 0), (Element[right, i], 0), (Element[right, i], Element[leftheights, i]), (Element[left, i], Element[leftheights, i])], i, 1, n) → leftRect
  9. IntegralBetween(((-(x(l) / y(l))) * x) - z(l) / y(l), f, x(B), x(A)) → Area

AI Drawing Prompt Reference

Draw a function curve with rectangles below to estimate the area under it. Adjust a slider to change the number of rectangles, showing how left and right rectangles approximate the area. Include the function curve, left and right rectangles, the integration interval, and the total area value. Start with the function curve and integration interval, then create left and right rectangles, and finally calculate and display the total area.
The prompt above was compiled from the original drawing commands and is for reference only.