Let E be the solid region in the first octant bounded from the sides by the cones and from above by the sphere z = √√x² + y² and z= This solid has mass density Obl 04 8(x, y, z) = z. Set up a triple integral in spherical coordinates that gives the total mass of this solid. O 2²+3² +2²= 3. 3 √²³√² + y²³₁ 3 Total mass = Total mass= √3 **/2 [² p² cos sin dødedp √3 2π ³12 pcos sin død0dp **/4 0 π/6 √3 /2/3 101
Let E be the solid region in the first octant bounded from the sides by the cones and from above by the sphere z = √√x² + y² and z= This solid has mass density Obl 04 8(x, y, z) = z. Set up a triple integral in spherical coordinates that gives the total mass of this solid. O 2²+3² +2²= 3. 3 √²³√² + y²³₁ 3 Total mass = Total mass= √3 **/2 [² p² cos sin dødedp √3 2π ³12 pcos sin død0dp **/4 0 π/6 √3 /2/3 101
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:Let E be the solid region in the first octant bounded from the sides by the cones
and from above by the sphere
This solid has mass density
Obl
2
z = √² + y² and z=
04
Od
8(x, y, z) = z.
Set up a triple integral in spherical coordinates that gives the total mass of this solid.
O el
x² + y² +2²= 3.
Total mass =
√3 /2/3
= 1.5¹² ³0.
*/4
Total mass =
Total mass=
Total mass
√√3
3
√3
2π
V.³ 1.² 1.74
10
π/6
Total mass
Total mass=
0
p²
x² + y²,
√3 T/2 T/3
cos Ф sin + dфd0dp
/6
cos o sin o dod0dp
p³ cose sin o dod0dp
π/2
/4
**** p sin dødodp
√3
p/2 AX/4
1.² 1.² ².
pcos sin o dod0dp
#/2 #/3
[*** [** p*cost sau² o dod@dp
w/4
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