Volume of Revolution Discussion (ii)b: Interactive Integral Demo

Volume of Revolution Discussion (ii)b: Interactive Integral Demo
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2017-11-01 14:04
① This GeoGebra example demonstrates how the volume of a solid of revolution is computed via definite integration, with interactive sliders and input fields for real-time exploration. ② Core mathematical concepts include the disk/washer method, volume by integration, parametric bounds, and the relationship between function graphs and generated solids. ③ Construction highlights: the Surface command creates the 3D solid, Textfield and InputBox1 allow user-defined parameters, Integral computes the definite integral, objects a, b, α set integration limits or rotation angle, g and f define the functions, V outputs the volume, and text1 provides explanatory labels. ④ Suitable for senior high school or introductory college calculus students, this example helps visualize the geometric meaning of volume integrals and supports classroom discussion or self-study.

GeoGebra Commands & Parameters

  1. Surface(f, α) → c
  2. Textfield(g) → InputBox1
  3. Integral((π * g(x)^(2)), a, b) → V