If you wish to integrate a function over the top half of the unit ball using spherical coordinates, its clear that if we describe the region of integration, p will run from 0 to 1, but what about θ and φ? 0 0 < 0 < Σπ 0 ΣΦ Σπ 0 < θ Σπ Ο Σ Φ < Σπ 0 0 < θ < 2π 0 < p < π/2 © 0 <0 <π/2 Ο Σ Φ < 2π © 0 < θ < 2π – ΣΦΩ Elev
If you wish to integrate a function over the top half of the unit ball using spherical coordinates, its clear that if we describe the region of integration, p will run from 0 to 1, but what about θ and φ? 0 0 < 0 < Σπ 0 ΣΦ Σπ 0 < θ Σπ Ο Σ Φ < Σπ 0 0 < θ < 2π 0 < p < π/2 © 0 <0 <π/2 Ο Σ Φ < 2π © 0 < θ < 2π – ΣΦΩ Elev
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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Transcribed Image Text:If you wish to integrate a function over the top half of the unit ball using spherical coordinates, its
clear that if we describe the region of integration, p will run from 0 to 1, but what about θ and φ?
0 0 < 0 < Σπ
0 ΣΦ Σπ
0 < θ Σπ
Ο Σ Φ < Σπ
0 0 < θ < 2π
0 < p < π/2
© 0 <0 <π/2
Ο Σ Φ < 2π
© 0 < θ < 2π
– ΣΦΩ
Elev
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