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 region Rexpressed in the function yz over spherical coordinates. Select one: *ア=2 »0=m/2 p² dr sin 0 cos 0 do sin ø do Jァ-0 =0 ア=2 p* dr •0=T/2 sin 0 cos 0 do sin o do Jr=0 0=0 0=T/2 cr=1 „2 dr rゆ=T/2 sin 0 cos 0 dO sin o dø r=0 0=0 0=T/2 pr=1 4 •$=r/2 sin? 0 cos 0 do p* dr r=0 sin ø do 0=0 ゆ=T/2 sin o do pr%3D2 sin? 0 cos 0 do =0 dr r=0 0=0
A sphere of radius 2 is centered on the origin. Consider the region R that consists of the octant of this sphere with x > 0, y > 0 and z > 0. Select the option that gives the volume integral of the region Rexpressed in the function yz over spherical coordinates. Select one: *ア=2 »0=m/2 p² dr sin 0 cos 0 do sin ø do Jァ-0 =0 ア=2 p* dr •0=T/2 sin 0 cos 0 do sin o do Jr=0 0=0 0=T/2 cr=1 „2 dr rゆ=T/2 sin 0 cos 0 dO sin o dø r=0 0=0 0=T/2 pr=1 4 •$=r/2 sin? 0 cos 0 do p* dr r=0 sin ø do 0=0 ゆ=T/2 sin o do pr%3D2 sin? 0 cos 0 do =0 dr r=0 0=0
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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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 yz over the region R expressed in
spherical coordinates.
Select one:
r=2
p2 dr
sin 0 cos 0 do
sin o do
r=0
0-0
=0
r=2
•0=n/2
p3 dr
sin 0 cos 0 do
sin ø dø
r=0
0=0
=0
r=1
p2 dr
sin 0 cos 0 dO
sin o dø
0-0
» r=1
rø=n/2
r* dr
0=0
„4
sin? 0 cos 0 dO
sin ø do
r=0
cr=D2
4 dr
sin? 0 cos 0 dO
sin ø do
0=0
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