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Volume of Revolution of ln(x) around x-axis

Volume of Revolution of ln(x) around x-axis
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2017-02-25 22:43
FunctionSolid GeometryIntegral
This example demonstrates the volume of a solid of revolution formed by rotating the graph of ln(x) around the x-axis. Key mathematical concepts include integration and the calculation of volumes of solids of revolution. Using commands like Rotate, Segment, and Integral, the volume of the solid can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Rotate(g, a°, xAxis) → b
  2. Segment(A, B) → h
  3. Rotate(A, a°, xAxis) → A'
  4. Rotate(B, a°, xAxis) → B'
  5. Segment(A', B') → h'
  6. Integral((π * f(x)^(2)), 1, (2 * ℯ)) → d

AI Drawing Prompt Reference

Draw the solid of revolution formed by rotating the curve of ln(x) around the x-axis, demonstrating the concept of integral calculation and volume of solids of revolution. Start by plotting the curve of ln(x), then rotate it around the x-axis to create a surface. The region enclosed by the rotated surface and the x-axis is used to calculate the volume with an integral. Finally, connect key points with line segments to show the rotation process and the volume calculation result.
The prompt above was compiled from the original drawing commands and is for reference only.