Use direct integration to find the centroid of the area shown in terms of a and h. y = kx² (a,h) X

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Shape
Triangular area
Quarter-circular
area
Semicircular area
Quarter-elliptical
area
Semielliptical
area
Semiparabolic
area
Parabolic area
Parabolic spandrel
General spandrel
Circular sector
Shape
Quarter-circular
arc
Semicircular are
Arc of circle
IZI
10월가을에
43L
|---
0
HI
F
y=kx2
X
C•
y=kx"
|——I.
C₁
ța
0|
X.
oa
0
13
h
ty!
C
DA
4
b
T
x
0
3π
0
3a
0
n+
n+2
2r sin a
3a
X
2r
0
r sin a
a
y
45
4b
3π
4b
3π
315
3h
10
n+1h
4n+2
0
y
ak
2/1/
k
0
Area
bh
T²
Rab
4
Kab
2ah
4ah
3
ah
ah
n+1
T
Length
플
MY
2ar
Transcribed Image Text:Shape Triangular area Quarter-circular area Semicircular area Quarter-elliptical area Semielliptical area Semiparabolic area Parabolic area Parabolic spandrel General spandrel Circular sector Shape Quarter-circular arc Semicircular are Arc of circle IZI 10월가을에 43L |--- 0 HI F y=kx2 X C• y=kx" |——I. C₁ ța 0| X. oa 0 13 h ty! C DA 4 b T x 0 3π 0 3a 0 n+ n+2 2r sin a 3a X 2r 0 r sin a a y 45 4b 3π 4b 3π 315 3h 10 n+1h 4n+2 0 y ak 2/1/ k 0 Area bh T² Rab 4 Kab 2ah 4ah 3 ah ah n+1 T Length 플 MY 2ar
Use direct integration to find the centroid of the area shown in terms of a and h.
y = kx²
(a,h)
X
Transcribed Image Text:Use direct integration to find the centroid of the area shown in terms of a and h. y = kx² (a,h) X
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