Multiple Integrals Example in Spherical Coordinates

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2019-05-08 06:22

This example demonstrates the application of multiple integrals using spherical coordinates. It shows how to calculate the volume of a specific region in 3D space using spherical coordinates. The Surface command is used to construct the 3D graph. Suitable for teaching multiple integrals in calculus courses.

GeoGebra Commands & Parameters

Surface(((a_2 * sin(ϕ)) * cos(θ)), ((a_2 * sin(ϕ)) * sin(θ)), (a_2 * cos(ϕ)), θ, 0, (b1 * π), ϕ, 0, (c1 * π)) → a_1
Surface(((t * sin((c1 * π))) * cos(θ)), ((t * sin((c1 * π))) * sin(θ)), (t * cos((c1 * π))), θ, 0, (b1 * π), t, 0, a_2) → b_1
Surface((ρ * sin(ϕ)), ((ρ * sin(ϕ)) * 0), (ρ * cos(ϕ)), ρ, 0, a_2, ϕ, 0, (c1 * π)) → d
Surface(((ρ * sin(ϕ)) * cos((b1 * π))), ((ρ * sin(ϕ)) * sin((b1 * π))), (ρ * cos(ϕ)), ρ, 0, a_2, ϕ, 0, (c1 * π)) → e

AI Drawing Prompt Reference

Draw a 3D graph demonstrating the application of multiple integrals in spherical coordinates, showing how to calculate the volume of a specific region. Start by plotting a surface defined by spherical coordinates, then add another surface for the integral's limits, followed by a conical surface, and finally a rotating surface. The combined surfaces form a complex solid figure suitable for teaching integral calculations.

The prompt above was compiled from the original drawing commands and is for reference only.