(b). Given y=8x²°, y=0, x = 1₁ first we find the area! 8x3 A = SS dA I fox³ dydx [ [y] 8x³² dx = 8 (²x³dx =) A = 1. A = 8. 12/²7/1 Ix= 312 [#²] J you => [A=2] Now, moment of inertia about x-axis! Ix = Say²da =) S fox³yzdydx 8x3 3 ( [9³] 8x dx = 510 (x1de x9dx - 5 512 Ty = √₁₂²dA =) 3X10 moment of inertia about y-axis! youx? = 128 (2) →) Tx= 128-A 8x3 Só joz xezdydz x=1 [²x², jyye²de = 8 ('xsde [y] 8x3 xSdx 6 Iy = 8.1 ²² 1² ⇒ & = 4 8 6
(b). Given y=8x²°, y=0, x = 1₁ first we find the area! 8x3 A = SS dA I fox³ dydx [ [y] 8x³² dx = 8 (²x³dx =) A = 1. A = 8. 12/²7/1 Ix= 312 [#²] J you => [A=2] Now, moment of inertia about x-axis! Ix = Say²da =) S fox³yzdydx 8x3 3 ( [9³] 8x dx = 510 (x1de x9dx - 5 512 Ty = √₁₂²dA =) 3X10 moment of inertia about y-axis! youx? = 128 (2) →) Tx= 128-A 8x3 Só joz xezdydz x=1 [²x², jyye²de = 8 ('xsde [y] 8x3 xSdx 6 Iy = 8.1 ²² 1² ⇒ & = 4 8 6
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![(b). Given y=8x³, y=0, x=1
first we find the area!
A = SS dA
Lo fox³ dydx
2
8x3
=)A=
{ [y] oe' de = 8√' x³dx
['
A = 8. 12/²7/1
[A=2
Now, moment of inertia about x-axis!
Ix = Sfa²dA =) ( 18x³y2dydx
3 [19³] 8* dx = 50 (²x²+²x
8x3
x9dx
1
10
Ix= 313 [7²]
yosu
J.
you
512
3X10
Ty = √√x²dA =)
moment of inertia about y-axis!
2
[x². [yj³x³ de
L'xz
· 128 . (2) -) Tx²= 128-A
=
15
Jó
I 18x³ xzdydz
=
8 5 x 5 x
x==1
Iy = 8.1 ²7 1
6
=) Ty = // = ²/3 (2) =) | Ty= 3 A
4
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7bd81766-0103-4cb8-b3e9-5180278339b3%2F7a4b83ee-25bb-4278-a6a6-2b1a4f0b583d%2Ffwcgbtr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b). Given y=8x³, y=0, x=1
first we find the area!
A = SS dA
Lo fox³ dydx
2
8x3
=)A=
{ [y] oe' de = 8√' x³dx
['
A = 8. 12/²7/1
[A=2
Now, moment of inertia about x-axis!
Ix = Sfa²dA =) ( 18x³y2dydx
3 [19³] 8* dx = 50 (²x²+²x
8x3
x9dx
1
10
Ix= 313 [7²]
yosu
J.
you
512
3X10
Ty = √√x²dA =)
moment of inertia about y-axis!
2
[x². [yj³x³ de
L'xz
· 128 . (2) -) Tx²= 128-A
=
15
Jó
I 18x³ xzdydz
=
8 5 x 5 x
x==1
Iy = 8.1 ²7 1
6
=) Ty = // = ²/3 (2) =) | Ty= 3 A
4
3
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