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Volume of Revolution - Disk/Washer Method about x-axis

Volume of Revolution - Disk/Washer Method about x-axis
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2020-12-18 06:24
Solid GeometryCalculusIntegral
This example demonstrates how to calculate the volume of a solid of revolution using the disk/washer method around the x-axis. Key mathematical concepts include integration and solid geometry. Functions f and g are constructed, and input boxes set the limits, with the Surface command used to generate the solid. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Intersect(f(x), g(x), 1) → A
  2. Intersect(f(x), g(x), 2) → B
  3. Textfield(f) → InputBoxF
  4. Textfield(g) → inputBoxG
  5. Segment(C, D) → h
  6. Circle((r, 0), C, xAxis) → c
  7. Circle((r, 0), D, xAxis) → d
  8. Surface(r, ((u * f(r)) * cos(t)), ((u * f(r)) * sin(t)), u, g(r) / f(r), 1, t, 0, (2 * π)) → e
  9. Surface(u, (f(u) * cos(t)), (f(u) * sin(t)), u, LB, UB, t, 0, (2 * π)) → i
  10. Surface(u, (g(u) * cos(t)), (g(u) * sin(t)), u, LB, UB, t, 0, (2 * π)) → j
  11. Surface(LB, ((u * f(LB)) * cos(t)), ((u * f(LB)) * sin(t)), u, g(LB) / f(LB), 1, t, 0, (2 * π)) → k
  12. Surface(UB, ((u * f(UB)) * cos(t)), ((u * f(UB)) * sin(t)), u, g(UB) / f(UB), 1, t, 0, (2 * π)) → l
  13. Textfield(LB) → inputBoxLB
  14. Textfield(UB) → InputBoxUB
  15. Surface(r, ((u * g(r)) * cos(t)), ((u * g(r)) * sin(t)), u, f(r) / g(r), 1, t, 0, (2 * π)) → n

AI Drawing Prompt Reference

Draw a solid of revolution using the disk/washer method around the x-axis. Start by plotting two functions, set the integration limits, and then display the solid formed by rotating each function around the x-axis. Highlight the inner and outer solids, as well as the solid generated by the region between the two curves. Use distinct colors for different parts and label the function expressions and integration limits.
The prompt above was compiled from the original drawing commands and is for reference only.