8 Nov 2021
Problem 51a
Page 475
Section 6.6: Applications to Physics and Engineering
Chapter 6: Application of Integration
Textbook ExpertVerified Tutor
8 Nov 2021
Given information
The two curves are 
and 
and the interval on the 
-axis is 
.
The function 
is always greater than the function 
for all values of in the interval.
Step-by-step explanation
Step 1.
Divide the area between the two curves into several vertical rectangles of width 
such that the height of each such rectangle at any value of is 
.
The centroid of such a rectangle is located at half the height.
So, its center of mass is at 
.
Now, the moments 
,
are the sum of the moments of all the individual rectangles about the respective axes.
So,
Therefore obtain the coordinate of the centroid 
.
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
Chapter
Section
- Problem 1
- Problem 2
- Problem 3
- Problem 4
- Problem 5
- Problem 6
- Problem 7a
- Problem 7b
- Problem 8
- Problem 9
- Problem 10
- Problem 11b
- Problem 11b
- Problem 12
- Problem 14
- Problem 15
- Problem 16
- Problem 17
- Problem 18
- Problem 19
- Problem 20
- Problem 21
- Problem 22
- Problem 23
- Problem 24
- Problem 25
- Problem 26
- Problem 28a
- Problem 28b
- Problem 29a
- Problem 29b
- Problem 29c
- Problem 30a
- Problem 30b
- Problem 30c
- Problem 31
- Problem 32
- Problem 33
- Problem 34
- Problem 35
- Problem 36
- Problem 37
- Problem 38
- Problem 39b
- Problem 39c
- Problem 39d
- Problem 40
- Problem 41
- Problem 42
- Problem 43
- Problem 44
- Problem 45
- Problem 46
- Problem 47
- Problem 48
- Problem 49
- Problem 50
- Problem 51a
- Problem 51b
- Problem 52a
- Problem 52b
- Problem 52c