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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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

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.

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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