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106–111. Surfaces of revolution Let C be the curve x = f(t), y = g(t), for a < t < b, where f' and g' are continuous on [a, b] and C does not intersect itself, except possibly at its endpoints. If g is nonnegative on [a, b], then the area of the surface obtained by revolving C about the x-axis is s = ["27g(1)Vf'(1)² + g'(1)² đt. Likewise, if f is nonnegative on [a, b], then the area of the surface obtained by revolving C about the y-axis is s = [2mf(1)Vf'(1)² + g'(1)° dt. Use the parametric equations of a semicircle of radius 1, x = cos t, y = sin t, for 0

106–111. Surfaces of revolution Let C be the curve x = f(t), y = g(t), for a < t < b, where f' and g' are continuous on [a, b] and C does not intersect itself, except possibly at its endpoints. If g is nonnegative on [a, b], then the area of the surface obtained by revolving C about the x-axis is s = ["27g(1)Vf'(1)² + g'(1)² đt. Likewise, if f is nonnegative on [a, b], then the area of the surface obtained by revolving C about the y-axis is s = [2mf(1)Vf'(1)² + g'(1)° dt. Use the parametric equations of a semicircle of radius 1, x = cos t, y = sin t, for 0

Calculus: Early Transcendentals
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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106–111. Surfaces of revolution Let C be the curve x = f(t), y = g(t), for a < t < b, where f' and g' are continuous on [a, b] and C does not intersect itself, except possibly at its endpoints. If g is nonnegative on [a, b], then the area of the surface obtained by revolving C about the x-axis is s = ["27g(1)Vf'(1)² + g'(1)² đt. Likewise, if f is nonnegative on [a, b], then the area of the surface obtained by revolving C about the y-axis is s = [2mf(1)Vf'(1)² + g'(1)° dt. Use the parametric equations of a semicircle of radius 1, x = cos t, y = sin t, for 0 <tS n, to verify that surface area of a unit sphere is 47.
Transcribed Image Text:106–111. Surfaces of revolution Let C be the curve x = f(t), y = g(t), for a < t < b, where f' and g' are continuous on [a, b] and C does not intersect itself, except possibly at its endpoints. If g is nonnegative on [a, b], then the area of the surface obtained by revolving C about the x-axis is s = ["27g(1)Vf'(1)² + g'(1)² đt. Likewise, if f is nonnegative on [a, b], then the area of the surface obtained by revolving C about the y-axis is s = [2mf(1)Vf'(1)² + g'(1)° dt. Use the parametric equations of a semicircle of radius 1, x = cos t, y = sin t, for 0 <tS n, to verify that surface area of a unit sphere is 47.
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