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Let C be the curve x = f(t), y = g(t), for ast≤ b, where f' and g' are continuous on [a, b] and C does not intersect itself, except possible at its endpoints. If g is nonnegative on [a, b], the area of the surface obtained by revolving C about the x-axis is S = 2r g(t)√f(t)² + g'(t)² dt. Likewise, if f is nonnegative a on [a, b], then the area of the surface obtained by revolving C about the y-axis is S = 2x f(t),√/f' (t)² + g' (t)² dt. a Find the area of the surface obtained by revolving one arch of the cycloid x= 12t - 12 sint, y = 12-12 cost, for 0 st≤ 2, about the x-axis.

Let C be the curve x = f(t), y = g(t), for ast≤ b, where f' and g' are continuous on [a, b] and C does not intersect itself, except possible at its endpoints. If g is nonnegative on [a, b], the area of the surface obtained by revolving C about the x-axis is S = 2r g(t)√f(t)² + g'(t)² dt. Likewise, if f is nonnegative a on [a, b], then the area of the surface obtained by revolving C about the y-axis is S = 2x f(t),√/f' (t)² + g' (t)² dt. a Find the area of the surface obtained by revolving one arch of the cycloid x= 12t - 12 sint, y = 12-12 cost, for 0 st≤ 2, about the x-axis.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.3: Maxima And Minima
Problem 27E
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Let C be the curve x = f(t), y = g(t), for ast≤ b, where f' and g' are continuous on [a, b] and C does not intersect itself, except possible at its endpoints. If g is nonnegative on [a, b], the area of the surface obtained by revolving C b about the x-axis is S=2л g(t)√√f'(t)² + g'(t)² dt. Likewise, if f is nonnegative a on [a, b], then the area of the surface obtained by revolving C about the y-axis is S = 2n f(t),√/f' (t)² + g' (t)² dt. 12₁ Find the area of the surface obtained by revolving one arch of the cycloid x = 12t - 12 sint, y = 12 - 12 cost, for 0 st≤2, about the x-axis.
Transcribed Image Text:Let C be the curve x = f(t), y = g(t), for ast≤ b, where f' and g' are continuous on [a, b] and C does not intersect itself, except possible at its endpoints. If g is nonnegative on [a, b], the area of the surface obtained by revolving C b about the x-axis is S=2л g(t)√√f'(t)² + g'(t)² dt. Likewise, if f is nonnegative a on [a, b], then the area of the surface obtained by revolving C about the y-axis is S = 2n f(t),√/f' (t)² + g' (t)² dt. 12₁ Find the area of the surface obtained by revolving one arch of the cycloid x = 12t - 12 sint, y = 12 - 12 cost, for 0 st≤2, about the x-axis.
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