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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:

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed...
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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:
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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