39-44. Shell method about other lines Let R be the region bounded by y=x2,x=1, and y=0. Use C 39. X=-2 40. X=1 41. X=2 42. y=1 43. y=-2

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The problem is on the screen and the answers are on the paper. My question is, when comparing 41 and 43, why do we do 1-(y)^1/2 (circled in pink) in this one and not in number 41. Basically why don't we subtract the right function from the left function in 41, and how do I know when to do this when revolving about other lines?

39-44. Shell method about other lines Let R be the region bounded by y=x,x=1, and y= 0 Use t
39. X=-2
40. X 1
41. X=2
42. y=1
43. y=-2
Transcribed Image Text:39-44. Shell method about other lines Let R be the region bounded by y=x,x=1, and y= 0 Use t 39. X=-2 40. X 1 41. X=2 42. y=1 43. y=-2
6.4.41 V = 2T
0.
(2-x)x² dx
= 27
(2x2- a) da
2x3
1
5T
%3D
0.
%3D2T
3.
4
0.
6.4.42
r1
V = 27
(1- y)(1- vT) dy = 27
(1- Vỹ - y + y%/2) dy
0.
2y3/2
y2
1
27 y
2y5/2!
1
2.
=2T 1.
3.
|
%3D
3
15
6.4.43
1.
2y5/2/ 4y3/2
+ 2y
,2
V = 2T
| (y + 2)(1 – Vỹ) dy = 27
(y +2-y3/2 - 2y/2) dy = 2n
%3D
%3D
0.
0.
3
01
4.
23T
2.
+2
%3D2T
3.
15
Transcribed Image Text:6.4.41 V = 2T 0. (2-x)x² dx = 27 (2x2- a) da 2x3 1 5T %3D 0. %3D2T 3. 4 0. 6.4.42 r1 V = 27 (1- y)(1- vT) dy = 27 (1- Vỹ - y + y%/2) dy 0. 2y3/2 y2 1 27 y 2y5/2! 1 2. =2T 1. 3. | %3D 3 15 6.4.43 1. 2y5/2/ 4y3/2 + 2y ,2 V = 2T | (y + 2)(1 – Vỹ) dy = 27 (y +2-y3/2 - 2y/2) dy = 2n %3D %3D 0. 0. 3 01 4. 23T 2. +2 %3D2T 3. 15
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