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Triple Integral in Cylindrical Coordinates by Joseph Manthey

Triple Integral in Cylindrical Coordinates by Joseph Manthey
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2016-11-22 22:20
TrigonometryCoordinate GeometrySolid GeometryCalculusIntegral
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
This example demonstrates the geometric interpretation of calculating a triple integral in cylindrical coordinates, visualizing the integral region and the function graph. Core math concepts include cylindrical coordinates, triple integrals, volume calculation, and polar coordinate transformation. Construction highlights involve using GeoGebra commands like Surface, Segment, and Polygon to build the integral region and function graph. Suitable for high school students and above to learn the geometric meaning of multiple integrals, and for calculus teaching demonstrations.

GeoGebra Commands & Parameters

  1. Surface(((f(θ) * cos(θ)) * r), ((f(θ) * sin(θ)) * r), 0, θ, 0, π, r, 0, 1) → bottom
  2. Surface((f(θ) * cos(θ)), (f(θ) * sin(θ)), (((-r) * f(θ)) * sin(θ)), θ, 0, π, r, 0, 1) → sides
  3. Surface(((f(θ) * cos(θ)) * r), ((f(θ) * sin(θ)) * r), (((-r) * f(θ)) * sin(θ)), θ, 0, π, r, 0, 1) → top
  4. Segment(A, A + (r * (B - A))) → segment
  5. Polygon({O, C, D}) → Polygon1
  6. Polygon({O, E, F}) → Polygon2