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3. Consider the iterated integral 1 = ƒƒ³*³*³ 3r dz dr de 0 Denote by G the solid of integration of the integral I, which is bounded by a portion of a sphere S₁ and a circular cylinder S₂. a) Sketch the solid G. b) Find an equation in spherical coordinates for S₂. c) Use a triple integral in spherical coordinates to show that I = 4. 2√5 √20-1²

3. Consider the iterated integral 1 = ƒƒ³*³*³ 3r dz dr de 0 Denote by G the solid of integration of the integral I, which is bounded by a portion of a sphere S₁ and a circular cylinder S₂. a) Sketch the solid G. b) Find an equation in spherical coordinates for S₂. c) Use a triple integral in spherical coordinates to show that I = 4. 2√5 √20-1²

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 17T
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3. Consider the iterated integral TT 2√5 √20-r² I = 3r dz dr de 0 Denote by G the solid of integration of the integral I, which is bounded by a portion of a sphere S₁ and a circular cylinder S₂. a) Sketch the solid G. b) Find an equation in spherical coordinates for S₂. c) Use a triple integral in spherical coordinates to show that I = 4π.
Transcribed Image Text:3. Consider the iterated integral TT 2√5 √20-r² I = 3r dz dr de 0 Denote by G the solid of integration of the integral I, which is bounded by a portion of a sphere S₁ and a circular cylinder S₂. a) Sketch the solid G. b) Find an equation in spherical coordinates for S₂. c) Use a triple integral in spherical coordinates to show that I = 4π.
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