[15] (3) GIVEN: a>0, a constant. Q: z = a²-x² W is the solid below the surface, and above the xy - plane. Consider the function [x² + y² f:W CR³ R, f(x, y, z) = 2 FIND: √a²-(x² + y²) dxdydz HINT: A(A¹) = A³/ y², Add extra pages, as needed. x C a is in xy-plane Y
[15] (3) GIVEN: a>0, a constant. Q: z = a²-x² W is the solid below the surface, and above the xy - plane. Consider the function [x² + y² f:W CR³ R, f(x, y, z) = 2 FIND: √a²-(x² + y²) dxdydz HINT: A(A¹) = A³/ y², Add extra pages, as needed. x C a is in xy-plane Y
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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for the first image attach please do the calculations similar to the second image attach
please please answer every correctly also this is not a graded question I would really appreciate if you would answer
![[15] (3) GIVEN: a>0, a constant. Q: z = a²-x² - y²,
W is the solid below the surface, Q
and above the ry - plane.
Consider the function
f:WCR³ → R, f(x,y,z) = √x² + y²
FIND: √x² + y² dxdydz
W
T:W*
| det DT|= r
≤2π
W*. = {(1,0,2)/05 + 5 aer²}
•2xra
T=CYL
√√√√ = ² + y² sydt = √r-v drdodz
r.r
-
4
15
0
a is in ry-plane
q²_p²
r² dzdrdo
drdo = 27 / ² r²[² / 4²
a
dr
2x [ + ²(a²_r²) dr = 27[^ªa²³r²_rªh
2x [ta²²² 4 + ²
²0
πα5
y
= 25 (₁²²²)
a
On the
surface,
Ω, z is
not
constant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa833a647-b9ad-4697-b42a-39aaf6365497%2Fc44bbe96-7028-4c9e-bcae-80d58c54a179%2F28idqdo_processed.png&w=3840&q=75)
Transcribed Image Text:[15] (3) GIVEN: a>0, a constant. Q: z = a²-x² - y²,
W is the solid below the surface, Q
and above the ry - plane.
Consider the function
f:WCR³ → R, f(x,y,z) = √x² + y²
FIND: √x² + y² dxdydz
W
T:W*
| det DT|= r
≤2π
W*. = {(1,0,2)/05 + 5 aer²}
•2xra
T=CYL
√√√√ = ² + y² sydt = √r-v drdodz
r.r
-
4
15
0
a is in ry-plane
q²_p²
r² dzdrdo
drdo = 27 / ² r²[² / 4²
a
dr
2x [ + ²(a²_r²) dr = 27[^ªa²³r²_rªh
2x [ta²²² 4 + ²
²0
πα5
y
= 25 (₁²²²)
a
On the
surface,
Ω, z is
not
constant.
![[15] (3) GIVEN: a>0, a constant. Q: z =
W is the solid below the surface,
and above the xy - plane.
Consider the function
3
2
f:WC R³ R, f(x, y, z) = √x² + y²
2
FIND: √a²-(x² + y²) dxdydz
W
a² - x² - y²,
HINT: A(AZ) = A ²/
Add extra
pages, as
needed.
X
Ω
Z
4 4 4 4
is in xy-plane Y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa833a647-b9ad-4697-b42a-39aaf6365497%2Fc44bbe96-7028-4c9e-bcae-80d58c54a179%2Fq2xc7cc_processed.png&w=3840&q=75)
Transcribed Image Text:[15] (3) GIVEN: a>0, a constant. Q: z =
W is the solid below the surface,
and above the xy - plane.
Consider the function
3
2
f:WC R³ R, f(x, y, z) = √x² + y²
2
FIND: √a²-(x² + y²) dxdydz
W
a² - x² - y²,
HINT: A(AZ) = A ²/
Add extra
pages, as
needed.
X
Ω
Z
4 4 4 4
is in xy-plane Y
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