For the part circled in red, my question is why is it 3-(y^2 +1)

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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For the part circled in red, my question is why is it 3-(y^2 +1)

Ex. 7 Find the volume of the solid generated by revolving the region between the parabola
Rotation About a Vertical Axis
Fnd the volume of the solid generated by revolving the region between the parabola
x= y +1 and the line x = 3 about the line x= 3.
Solution:
Parabola-line
R(y) 3- (y2 + 1)
= 2 - y?
dishribute
X R(y) = 2-y2
V2
(3, V2)
0.
1
3.
5
1
5.
x = y² + 1
* = y2 + 1
-V2
(3, -V2)
(b)
(a)
Cy)
dy
2
-Sa
131
4.
4y-
5.
The Washer Method-Rotation About the x-Axis
15
to generate a solid does not border on or cross the axis of revolution
Transcribed Image Text:Ex. 7 Find the volume of the solid generated by revolving the region between the parabola Rotation About a Vertical Axis Fnd the volume of the solid generated by revolving the region between the parabola x= y +1 and the line x = 3 about the line x= 3. Solution: Parabola-line R(y) 3- (y2 + 1) = 2 - y? dishribute X R(y) = 2-y2 V2 (3, V2) 0. 1 3. 5 1 5. x = y² + 1 * = y2 + 1 -V2 (3, -V2) (b) (a) Cy) dy 2 -Sa 131 4. 4y- 5. The Washer Method-Rotation About the x-Axis 15 to generate a solid does not border on or cross the axis of revolution
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