When the area between the curve y= x², 0

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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When the area between the curve y= x², 0<x<2 and the y-axis is rotated about the
y-axis, it forms a bowl-shaped solid of revolution. A student was asked to find the
volume of the bowl-shaped figure.
First, she used the disk method and found the volume to be
| nydy:
луду%3D 8л.
Next, she checked her work using the method of cylindrical shells and found the same
2лх(4 — х) dx %3D 8л.
answer:
Then, the student was asked to find “the value of x for which the volume would be half
the original volume." She immediately realized this wording left room for
ck
interpretation. So she first solved the equation | nydy:
1
= =
· 81 and found k = 2/2.
2
This is a y-value so the corresponding x-value is v2/2= 1.682. She again checked her
k
2nx(4-x²) dx = ;
1
· 81 and found that
work by shells by solving
k = V-2(v2-2) - 1.082. (This is the x-value.)
All computations are correct. Explain why her answers are different.
Transcribed Image Text:When the area between the curve y= x², 0<x<2 and the y-axis is rotated about the y-axis, it forms a bowl-shaped solid of revolution. A student was asked to find the volume of the bowl-shaped figure. First, she used the disk method and found the volume to be | nydy: луду%3D 8л. Next, she checked her work using the method of cylindrical shells and found the same 2лх(4 — х) dx %3D 8л. answer: Then, the student was asked to find “the value of x for which the volume would be half the original volume." She immediately realized this wording left room for ck interpretation. So she first solved the equation | nydy: 1 = = · 81 and found k = 2/2. 2 This is a y-value so the corresponding x-value is v2/2= 1.682. She again checked her k 2nx(4-x²) dx = ; 1 · 81 and found that work by shells by solving k = V-2(v2-2) - 1.082. (This is the x-value.) All computations are correct. Explain why her answers are different.
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