Problem

Refer to the figure and find the volume generated…

01:36

Problem 25 Hard Difficulty

Refer to the figure and find the volume generated by rotating the given region about the specified line.

$ \Re_2 $ about $ AB $

Answer

$\frac{13}{45} \pi$

More Answers

02:41

Wen Z.

Topics

Applications of Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 2

Volumes

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Watch More Solved Questions in Chapter 6

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

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 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Video Transcript

we know that in order to find the volume were integrating on the access parallel to the axis of rotation, you know, the axis of rotation is X equals one There for the outer radius is gonna be distance from X equals ear to the axis of rotation, which is one minus dear. We're just simply one. And then we know the inner radius is gonna be the distance from why did the fourth equals X to the axis of rotation? X equals one. So again, using the same reasons. Which means we have one minus y to the fourth for the inner now, or volume is pi times integral from 01 of the inner. Okay, so what we just did is we reason the formula pi times outer minus inner and outer and inner. Both individuals scored so one squared is one. This is also squared. So we foiled us. So we So we took this which is the inner. And then we spend them when you square it. Then you use the foil method, right? So now we can simplify before we find the integral. We have to simplify this to go to y to the fourth minus wide of the eighth. Do you? Why now we can integrate. Use the power method, which means increased the experiment by one and divide by the new exponents. We have zero for the second bound of when we plug ins. Here we get zero, which means our solution is 13 point over 45.

Amrita B.

Topics

Applications of Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 2

Volumes

Top Calculus 2 / BC Educators

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University