MathPlotAI Logo MathPlotAI

Fubini's theorem: Rectangular regions

Fubini's theorem: Rectangular regions
Loading the math board and drawing, please wait…
2022-08-04 08:12
CalculusGeometric ConstructionSlider Animation
Fubini's theorem demonstrates how to compute double integrals over rectangular regions. This concept involves calculus and integration, where the region is divided into smaller rectangles to evaluate the integral. The construction uses GeoGebra commands like Polygon, Segment, and Surface to create the rectangular area and function graphs. Suitable for high school students or college students learning calculus fundamentals, to understand the relationship between integration and geometry.

GeoGebra Commands & Parameters

  1. Polygon(P1, P2, P3, P4) → Pol1, p1, p2, p3, p4
  2. Segment((Px, Vy, 0), (Px, Vy, f(Px, Vy))) → PP1
  3. Segment((Vx, Py, 0), (Vx, Py, f(Vx, Py))) → PP2
  4. SelectedIndex(opt) → ind
  5. Surface(Vx, u, ((1 / 4 * t) * f(Vx, u)), u, c, Py, t, 0, 4) → S1
  6. Surface(u, Vy, ((1 / 4 * t) * f(u, Vy)), u, a, Px, t, 0, 4) → S2
  7. Segment((a, 0, 0), (a, c, 0)) → T1
  8. Segment((b, 0, 0), (b, c, 0)) → T2
  9. Segment((0, c, 0), (a, c, 0)) → T3
  10. Segment((0, d, 0), (a, d, 0)) → T4
  11. Surface(u, v, f(u, v), u, a, b, v, c, d) → S

AI Drawing Prompt Reference

Draw a rectangular region and calculate the double integral by dividing it into smaller rectangles. First, draw the four sides of the rectangle, then add two auxiliary lines, followed by drawing two surfaces, and finally add two line segments perpendicular to the x-axis and y-axis.
The prompt above was compiled from the original drawing commands and is for reference only.