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A sphere of radius 2 is centered on the origin. Consider the region R that consists of the octant of this sphere with x > 0, y > 0 and z> 0. Select the option that gives the volume integral of the function xy over the region R expressed in spherical coordinates. Select one: t=2 1² C f p² r=2 [². ³ dr Loo dr ² dr ² dr 0=π/2 dr +0=π/2 0=π/2 0-0 +0=π/2 +0=π/2 0-0 sin²0 de sin ³0 de sin²0 de sin²0 de sin ³0 de p=π/2 $=0 •=π/2 •=π/2 $=0 sin cos do sin cos o do sin cos o do sin o cos o do sin cos o do

A sphere of radius 2 is centered on the origin. Consider the region R that consists of the octant of this sphere with x > 0, y > 0 and z> 0. Select the option that gives the volume integral of the function xy over the region R expressed in spherical coordinates. Select one: t=2 1² C f p² r=2 [². ³ dr Loo dr ² dr ² dr 0=π/2 dr +0=π/2 0=π/2 0-0 +0=π/2 +0=π/2 0-0 sin²0 de sin ³0 de sin²0 de sin²0 de sin ³0 de p=π/2 $=0 •=π/2 •=π/2 $=0 sin cos do sin cos o do sin cos o do sin o cos o do sin cos o do

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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A sphere of radius 2 is centered on the origin. Consider the region R that consists of the octant of this sphere with x > 0, y > 0 and z> 0. Select the option that gives the volume integral of the function xy over the region R expressed in spherical coordinates. Select one: t=2 1² C dr sin ³0 de 0=π/2 for ² der for sin² 8 de (2-77 0-0 r=2 p² ³ dr Loo 0=π/2 ² dr +0=π/2 +0=π/2 sin²0 de p=π/2 sin²0 de $=0 •=π/2 •=π/2 sin cos do sin cos o do sin o cos o do $=0 +0=π/2 ²4 dr sin" 0 do f sin pi cos o de 0-0 sin cos o do
Transcribed Image Text:A sphere of radius 2 is centered on the origin. Consider the region R that consists of the octant of this sphere with x > 0, y > 0 and z> 0. Select the option that gives the volume integral of the function xy over the region R expressed in spherical coordinates. Select one: t=2 1² C dr sin ³0 de 0=π/2 for ² der for sin² 8 de (2-77 0-0 r=2 p² ³ dr Loo 0=π/2 ² dr +0=π/2 +0=π/2 sin²0 de p=π/2 sin²0 de $=0 •=π/2 •=π/2 sin cos do sin cos o do sin o cos o do $=0 +0=π/2 ²4 dr sin" 0 do f sin pi cos o de 0-0 sin cos o do
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