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Disc Method Calculus Demo

Disc Method Calculus Demo
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2018-11-21 10:15
Solid GeometryCalculusIntegralGeometric Construction
In collections GeoGebra 3D & AR: PreCalc & Calculus Resources
This example demonstrates the geometric process of calculating the volume of a solid of revolution using the disc method. It involves core calculus concepts like integration, volume calculation, and geometric transformations. Key GeoGebra commands and objects used include Polygon, Surface, RectangleSum, Sequence, Rotate, and Textfield for dynamic visualization and volume computation, suitable for high school students and calculus beginners.

GeoGebra Commands & Parameters

  1. Polygon(A, B, D, C) → q1, a_1, b_1, d, c
  2. Surface(1 + u, (y(C) * cos(v)), (y(C) * sin(v)), u, 0, 1, v, 0, α) → e
  3. Surface(x(B), ((u * y(D)) * cos(v)), ((u * y(D)) * sin(v)), u, 0, 1, v, 0, α) → f
  4. Surface(x(A), ((u * y(D)) * cos(v)), ((u * y(D)) * sin(v)), u, 0, 1, v, 0, α) → g
  5. RectangleSum(h, a, b, n, q) → i
  6. Sequence(Polygon[(a + (i * deltax), 0), (a + ((i + 1) * deltax), 0), (a + ((i + 1) * deltax), h(a + ((i + 1) * deltax))), (a + (i * deltax), h(a + ((i + 1) * deltax)))], i, 0, n - 1) → L_1
  7. Sequence(Surface[a + (i * deltax) + (deltax * u), (h(a + ((i + 1) * deltax)) * cos(v)), (h(a + ((i + 1) * deltax)) * sin(v)), u, 0, 1, v, 0, α], i, 0, n - 1, 1) → L_4
  8. Sequence(Surface[a + (i * deltax), ((h(a + ((i + 1) * deltax)) * cos(v)) * u), ((h(a + ((i + 1) * deltax)) * sin(v)) * u), u, 0, 1, v, 0, α], i, 0, n - 1, 1) → L_2
  9. Sequence(Surface[a + ((i + 1) * deltax), ((h(a + ((i + 1) * deltax)) * cos(v)) * u), ((h(a + ((i + 1) * deltax)) * sin(v)) * u), u, 0, 1, v, 0, α], i, 0, n - 1, 1) → L_3
  10. Rotate(L_1, α, xAxis) → L_5
  11. Textfield(a) → InputBox1
  12. Textfield(b) → InputBox2
  13. Textfield(n) → InputBox3
  14. Textfield(h) → InputBox4

AI Drawing Prompt Reference

Draw a solid of revolution formed by rotating a given function around the x-axis and calculate its volume using the rectangular approximation method. First, draw a quadrilateral, then rotate it around the x-axis to generate the surface of the solid. Next, use the rectangular approximation method by rotating a series of rectangles to approximate the volume of the solid. Finally, input the function expression, interval, and number of divisions through input boxes to dynamically adjust the shape and volume approximation of the solid.
The prompt above was compiled from the original drawing commands and is for reference only.