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Triple Integral in Spherical Coordinates by Brian Abbott

Triple Integral in Spherical Coordinates by Brian Abbott
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2017-04-03 03:42
TrigonometryCalculusIntegral
In collections intersection: surface-surface, curve-curve
This example demonstrates how to calculate a triple integral in spherical coordinates. Key mathematical concepts include spherical coordinates, triple integrals, and their geometric applications. Using GeoGebra commands such as Surface and Segment, users can visually understand the construction of the triple integral. Suitable for university mathematics students and researchers in related fields.

GeoGebra Commands & Parameters

  1. Surface(((f(ϕ) * sin(ϕ)) * cos(θ)), ((f(ϕ) * sin(ϕ)) * sin(θ)), (f(ϕ) * cos(ϕ)), ϕ, 0, π / 4, θ, 0, (2 * π)) → top
  2. Surface(((ρ * sin(π / 4)) * cos(θ)), ((ρ * sin(π / 4)) * sin(θ)), (ρ * cos(π / 4)), ρ, 0, cos(π / 4), θ, 0, (2 * π)) → bottom
  3. Segment(O, (r * A)) → segment
  4. Surface((((ρ * sin(ϕ)) * cos(π / 4)) * cos(ϕ)), (((ρ * sin(ϕ)) * sin(π / 4)) * cos(ϕ)), ((ρ * cos(ϕ)) * cos(ϕ)), ρ, 0, 1, ϕ, 0, s) → partition
  5. Surface((((ρ * sin(ϕ)) * cos(t)) * cos(ϕ)), (((ρ * sin(ϕ)) * sin(t)) * cos(ϕ)), ((ρ * cos(ϕ)) * cos(ϕ)), ρ, 0, 1, ϕ, 0, π / 4) → solid