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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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