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
Related questions
Concept explainers
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad530511-9758-42d9-9994-894bc4eea3f3%2F3f16515e-fd26-48ca-905c-ead28e6043d7%2Fy71peru_processed.png&w=3840&q=75)
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
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)