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Triple Integral in Rectangular Coordinates

Triple Integral in Rectangular Coordinates
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2020-02-20 13:09
Coordinate GeometrySolid GeometryIntegral
This example demonstrates triple integrals in rectangular coordinates. It constructs a 3D solid to illustrate the application of integration in three-dimensional space. Key mathematical concepts include triple integrals, solid geometry, and coordinate geometry. Commands used include Surface, Polygon, Vector, and others. Suitable for university-level calculus and solid geometry courses.

GeoGebra Commands & Parameters

  1. Surface(u, u^(2), ((4 - u^(2)) * v), u, -2, 2, v, 0, 1) → sides
  2. Surface((u * v), u^(2), 4 - u^(2), u, -2, 2, v, 0, 1) → top
  3. Segment(A, A + (r * (B - A))) → segment
  4. Polygon({C, D, F, E}) → FixedTriangle
  5. Polygon({G, H, I}) → poly1
  6. Surface((u * v), u^(2), 0, u, -2, 2, v, 0, 1) → bottom
  7. Vector((0, 1, 0), (0, 1, 5)) → u