A sphere of radius 3 is centred 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.
A sphere of radius 3 is centred 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.
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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Question
A sphere of radius 3 is centred 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.
Transcribed Image Text:*
r=3
P
r=3
r=0
nr=3
r=1
r=0
np=1
T=0
p²0² 10-0
r dr
•0=x/2
² dr
dr
0=π/2
0=0
0=π/2
0=0
0=π/2
sin²0 de
0=0
sin³0 de
3
0=π/2
you 18-0
dr sin ³0 de sino con do
O=T/2
sin²0 de
=0
•=π/2
sin³0 de
3
$=0
=π/2
$=0
L
=π/2
$=0
=π/2
sin cos o do
ľ
$=0
sin o cos do
sin cos do
sin o cos do
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