for the first image attach please do the calculations similar to the second image attachplease 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, Qand above the ry - plane.Consider the functionf:WCR³ → R, f(x,y,z) = √x² + y²FIND: √x² + y² dxdydzWT:W*| det DT|= r≤2πW*. = {(1,0,2)/05 + 5 aer²}•2xraT=CYL√√√√ = ² + y² sydt = √r-v drdodzr.r-4150a is in ry-planeq²_p²r² dzdrdodrdo = 27 / ² r²[² / 4²adr2x [ + ²(a²_r²) dr = 27[^ªa²³r²_rªh2x [ta²²² 4 + ²²0πα5y= 25 (₁²²²)aOn thesurface,Ω, z isnotconstant. [15] (3) GIVEN: a>0, a constant. Q: z =W is the solid below the surface,and above the xy - plane.Consider the function32f:WC R³ R, f(x, y, z) = √x² + y²2FIND: √a²-(x² + y²) dxdydzWa² - x² - y²,HINT: A(AZ) = A ²/Add extrapages, asneeded.XΩZ4 4 4 4is 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

[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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Question

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.

[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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