MathPlotAI Logo MathPlotAI

Double Integral Volume Demo by Rasha Tarek

Double Integral Volume Demo by Rasha Tarek
Loading the math board and drawing, please wait…
2020-02-09 10:45
Solid GeometryCalculusIntegralGeometric Construction
This example demonstrates the calculation of the volume of a solid with a curved top using double integrals. It involves core math concepts like definite integrals, integral calculus, volume computation, exponential functions, conic sections, area, and equations. The construction utilizes GeoGebra commands/objects such as Polygon, Textfield, Surface, Segment, Translate, and Rotate. Suitable for high school and above students to understand the application of integrals in geometry.

GeoGebra Commands & Parameters

  1. Polygon(D, B, L, M, C, A, E, F, G, H, I, J, K) → poly1, d, k, l, m, c_1, b, a_1, e, f_1, g, h, i, j
  2. Textfield(o) → InputBox1
  3. Textfield(t) → InputBox2
  4. Textfield(u) → InputBox3
  5. Textfield(v) → InputBox4
  6. Textfield(w) → InputBox5
  7. Surface(a, b, o(a, b), a, t, u, b, v, w) → a
  8. Segment((u, q, 0), (u, q, o(u, q))) → n
  9. Segment((t, q, 0), (t, q, o(t, q))) → r
  10. Segment((t, q), (u, q)) → s
  11. Translate(poly1, Vector[(0, 1, 0)]) → poly1'
  12. Translate(poly1, Vector[(0, pi)]) → poly2
  13. Rotate(poly2, pi) → poly3
  14. Translate(poly3, Vector[(0, 2)]) → poly3'