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Volumes generated by region between 2 curves

Volumes generated by region between 2 curves
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2019-01-28 17:20
FunctionSolid GeometryCalculusIntegralGeometric Construction
This example demonstrates the volume generated by rotating a region between two curves. It involves core math concepts like integration, volume calculation, function graphs, and rotational solids. Constructed using GeoGebra commands like Textfield, IntegralBetween, Surface, Integral, it allows parameter control via input boxes, volume calculation, and visualization of rotational bodies, making it suitable for high school and above students learning integral volume calculations and geometric applications of function graphs.

GeoGebra Commands & Parameters

  1. Textfield(f) → inputBox1
  2. Textfield(upperlimit) → inputBox2
  3. Textfield(lowerlimit) → inputBox3
  4. IntegralBetween(f, g, ll, ul) → h_1
  5. Textfield(g) → InputBox1
  6. IntegralBetween(f, g, ll, ul) → AreabyDefiniteIntegral
  7. Surface(u, (f(u) * cos(v)), (f(u) * sin(v)), u, ll, ul, v, 0, θ) → CurvedSurfacef
  8. Surface(u, (g(u) * cos(v)), (g(u) * sin(v)), u, ll, ul, v, 0, θ) → CurvedSurfaceg
  9. Surface(u, f(u) + (v * (g(u) - f(u))), 0, u, ll, ul, v, 0, 1) → Facexy
  10. Surface(u, ((f(u) + (v * (g(u) - f(u)))) * cos(θ)), ((f(u) + (v * (g(u) - f(u)))) * sin(θ)), u, ll, ul, v, 0, 1) → Facerotate
  11. Surface(ll, (u * cos(v)), (u * sin(v)), u, Min[f(ll), g(ll)], Max[f(ll), g(ll)], v, 0, θ) → LLface
  12. Surface(ul, (u * cos(v)), (u * sin(v)), u, Min[f(ul), g(ul)], Max[f(ul), g(ul)], v, 0, θ) → ULface
  13. Integral(f, ll, ul) → intf
  14. Integral(g, ll, ul) → intg
  15. Surface(u, ((v * f(u)) * cos(θ)), ((v * f(u)) * sin(θ)), u, ll, ul, v, 0, 1) → Facerotatef
  16. Surface(u, ((v * g(u)) * cos(θ)), ((v * g(u)) * sin(θ)), u, ll, ul, v, 0, 1) → Facerotateg
  17. Surface(u, (v * f(u)), 0, u, ll, ul, v, 0, 1) → Facexyf
  18. Surface(u, (v * g(u)), 0, u, ll, ul, v, 0, 1) → Facexyg
  19. Surface(ll, (u * cos(v)), (u * sin(v)), u, 0, f(ll), v, 0, θ) → LLfacef
  20. Surface(ll, (u * cos(v)), (u * sin(v)), u, 0, g(ll), v, 0, θ) → LLfaceg
  21. Surface(ul, (u * cos(v)), (u * sin(v)), u, 0, f(ul), v, 0, θ) → ULfacef
  22. Surface(ul, (u * cos(v)), (u * sin(v)), u, 0, g(ul), v, 0, θ) → ULfaceg
  23. Integral(f, ll, ul) → AreabyDefiniteIntegralf
  24. Integral(g, ll, ul) → AreabyDefiniteIntegralg

AI Drawing Prompt Reference

Visualize the volume generated by rotating a region between two curves. Start by plotting two function graphs and marking the integral bounds. Calculate the area between the curves using integration and generate the surface of the solid of revolution. Include auxiliary surfaces formed by the function curves and bounds, as well as the lateral and base surfaces of the solid, to create a complete model that illustrates integral volume calculations and the geometric application of function graphs.
The prompt above was compiled from the original drawing commands and is for reference only.