MathPlotAI Logo MathPlotAI

Area under a curve: sum of rectangles

Area under a curve: sum of rectangles
Loading the math board and drawing, please wait…
2019-11-13 22:45
FunctionCalculusIntegralGeometric Construction
This example demonstrates how to approximate the area under a curve using the sum of rectangles. It involves core math concepts like integration, rectangle sums, function graphs, and differential calculus. Constructed using GeoGebra commands LeftSum, NIntegral, Textfield, and objects like n, a, A, b, f, B, rectanglesum, integral, text1, text2, text3, InputBox1. Suitable for high school and above learning integral concepts and numerical integration methods.

GeoGebra Commands & Parameters

  1. LeftSum(f, a, b, n) → rectanglesum
  2. NIntegral(f, a, b) → integral
  3. Textfield(f) → InputBox1

AI Drawing Prompt Reference

Draw a function graph and plot several rectangles below it to demonstrate how the sum of rectangle areas approximates the integral, labeling the function expression, integral bounds, and both approximate and exact integral values to illustrate the geometric meaning of numerical integration and calculus.
The prompt above was compiled from the original drawing commands and is for reference only.