Problem

Refer to the figure and find the volume generated…

02:47

Problem 24 Hard Difficulty

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

$ \Re_2 $ about $ OC $

Answer

$\frac{\pi}{9}$

Top Calculus 2 / BC Educators

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

were given a figure and the figure. A region in a specified line. We have to find the volume generated by rotating this region about this line. The region is. The region are too. Can you rotate about the line formed by Oc? Yeah. An 82 year old. Uh huh. Stickball baseball hat on sq. That way that so looking at the figure, there's three parts. We have the curve. White holds one. You can be up or down. We have blue curve. The curve wife was the fourth root of X. Is a bound on the right and then we have victor's superintendent. The vertical boundary x equals zero on the left group. Now O. C. Is the same as Uh huh. Here, is that the line X equals zero. This is the same as irritating about he Y axis Duke, I'm the Earl of this. And therefore looking at a figure, we get a disc take solid. And so we'll use this method to find the volume. So we want to find the radius right away. It's easy to see that the radius is simply Y equals the fourth root of X. Or instead not 45 X, but three years is X equals Why It's A 4th. And so our volume by the disk method is the equals pi times the integral from Y equals 0 to 1 of our radius wide. The fourth square peg Dy. This isn't easy to grow to evaluate. Once you do, you should get the answer. Hi over nine. That what

Chris T.

Ohio State University

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 2

Volumes

Problem