5.25. Find (a) the area and (b) the moment of inertia about the y axis of the region in the xy plane bounded by y = 4 - x and the x axis. (a) Subdivide the region into rectangles as in Figure 5.1. A typical rectangle is shown in Figure 5.8. Then Required area = lim EfŠ,)Ax, k=1 = lim (4 - )Axę n kel = L (4 - x² )dx = 2 %3D 3 (b) Assuming unit density, the moment of inertia about the y axis of the typical rectangle shown in Figure 5.8 is f(5) Ax;. Then
5.25. Find (a) the area and (b) the moment of inertia about the y axis of the region in the xy plane bounded by y = 4 - x and the x axis. (a) Subdivide the region into rectangles as in Figure 5.1. A typical rectangle is shown in Figure 5.8. Then Required area = lim EfŠ,)Ax, k=1 = lim (4 - )Axę n kel = L (4 - x² )dx = 2 %3D 3 (b) Assuming unit density, the moment of inertia about the y axis of the typical rectangle shown in Figure 5.8 is f(5) Ax;. Then
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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5.25) my professor says I have to explain the steps in the solved problems in the picture. Not just copy eveything down from the text.
Transcribed Image Text:Applications (area, arc length, volume, moment of inertia)
5.25.
Find (a) the area and (b) the moment of inertia about the y axis of the region in the xy plane bounded by y =
4 – x and the x axis.
(a) Subdivide the region into rectangles as in Figure 5.1. A typical rectangle is shown in Figure 5.8. Then
n
Required area =
lim Ef5)Ax,
n 00
k=1
= lim (4 - )Ax,
n- 00
k=1
32
= L,(4 – x*)dx =
3
(b) Assuming unit density, the moment of inertia about the y axis of the typical rectangle shown in Figure 5.8
is f (5) Axy. Then
Ax-
2K
un
(-2, 0)
Šk
(2, 0)
Figure 5.8
Required moment of inertia = lim SGDAX, = lim š?(4 – )Ax,
n 00
k=1
n-00
k=1
128
= ,r*(4 – x²)dx =
15
- X
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