Let R be the region bounded by the curves y = 3x² -2 and y=2-x² Let S be the solid of revolution obtained by revolving the region R about the line = 3. The goal of this exercise is to compute the volume of S by using the method of cylindrical shells. a) Determine the smallest x-coordinate ₁ and the largest x-coordinate of the points in this region. #1 12 = b) Let a be a real number in the interval [1,2]. Consider a typical cylindrical shell of thickness Az obtained by revolving about the line x = 3 the thin strip of the region R that lies between x and x +Ax. For such a shell, find expressions for its approximate radius r(x) and its approximate height h(x). r(x) ≈ h(x)~ The volume of a typical shell as described above is approximately A (x)Ax. What is the function A (x)? A (x) = FORMATTING: Do not include the thickness Ax in your expression for A(x). c) Determine the volume of S with ±0.01 precision. Answer:
Let R be the region bounded by the curves y = 3x² -2 and y=2-x² Let S be the solid of revolution obtained by revolving the region R about the line = 3. The goal of this exercise is to compute the volume of S by using the method of cylindrical shells. a) Determine the smallest x-coordinate ₁ and the largest x-coordinate of the points in this region. #1 12 = b) Let a be a real number in the interval [1,2]. Consider a typical cylindrical shell of thickness Az obtained by revolving about the line x = 3 the thin strip of the region R that lies between x and x +Ax. For such a shell, find expressions for its approximate radius r(x) and its approximate height h(x). r(x) ≈ h(x)~ The volume of a typical shell as described above is approximately A (x)Ax. What is the function A (x)? A (x) = FORMATTING: Do not include the thickness Ax in your expression for A(x). c) Determine the volume of S with ±0.01 precision. Answer:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let R be the region bounded by the curves
y=2-x²
y = 3x² - 2 and
Let S be the solid of revolution obtained by revolving the region R about the line x = 3.
The goal of this exercise is to compute the volume of S by using the method of cylindrical shells.
a) Determine the smallest x-coordinate ₁ and the largest x-coordinate 2 of the points in this region.
x1
x2
b) Let a be a real number in the interval [#1, #2].
Consider a typical cylindrical shell of thickness Ax obtained by revolving about the line x = 3 the thin strip of the region R that
lies between x and x + Ax. For such a shell, find expressions for its approximate radius r(x) and its approximate height h(x).
r(x) ~
h(x) ~
RE
The volume of a typical shell as described above is approximately A (x)Ax. What is the function A (x)?
A (x)
=
FORMATTING: Do not include the thickness Ax in your expression for A(x).
c) Determine the volume of S with +0.01 precision.
Answer:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5280d48f-13d7-4d66-9538-46469380c983%2F21d66dc5-4ecb-40b0-ab10-99c508435165%2F6ju2zek_processed.png&w=3840&q=75)
Transcribed Image Text:Let R be the region bounded by the curves
y=2-x²
y = 3x² - 2 and
Let S be the solid of revolution obtained by revolving the region R about the line x = 3.
The goal of this exercise is to compute the volume of S by using the method of cylindrical shells.
a) Determine the smallest x-coordinate ₁ and the largest x-coordinate 2 of the points in this region.
x1
x2
b) Let a be a real number in the interval [#1, #2].
Consider a typical cylindrical shell of thickness Ax obtained by revolving about the line x = 3 the thin strip of the region R that
lies between x and x + Ax. For such a shell, find expressions for its approximate radius r(x) and its approximate height h(x).
r(x) ~
h(x) ~
RE
The volume of a typical shell as described above is approximately A (x)Ax. What is the function A (x)?
A (x)
=
FORMATTING: Do not include the thickness Ax in your expression for A(x).
c) Determine the volume of S with +0.01 precision.
Answer:
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