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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
Problem 70E
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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. 

*
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
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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