Explanation Formula used: Let C be the curve with the parametric equation x = f ( t ) , y = g ( t ) , for a ≤ t ≤ b , where f ′ and g ′ is continuous on [ a , b ] and C does not intersect itself, except possibly at its endpoints. Then, the area of the surface obtained by revolving C about the x -axis is, S = ∫ a b 2 π g ( t ) f ′ ( t ) 2 + g ′ ( t ) 2 d t The area of the surface obtained by revolving C about the y -axis is, S = ∫ a b 2 π f ( t ) f ′ ( t ) 2 + g ′ ( t ) 2 d t Calculation: The given parametric equation is x = cos 3 t , y = sin 3 t , for 0 ≤ t ≤ π 2 . Here, x = f ( t ) = cos 3 t and y = g ( t ) = sin 3 t . Differentiate f ( t ) and g ( t ) with respect to t as follows. f ′ ( t ) = d d t ( cos 3 t ) = − 3 cos 2 t sin t g ′ ( t ) = d d t ( sin 3 t ) = 3 sin 2 t cos t Substitute f ′ ( t ) = − 3 cos 2 t sin t and g ′ ( t ) = 3 sin 2 t cos t in S = ∫ a b 2 π g ( t ) f ′ ( t ) 2 + g ′ ( t ) 2 d t

MyLab Math with Pearson eText -- 24 Month Access -- for Calculus with Integrated Review

3rd Edition

ISBN: 9780135243435

Author: Bill Briggs

Publisher: Pearson Education (US)

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Chapter 12.1, Problem 108E

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The surface area of the curve x=cos3t,y=sin3t, for 0≤t≤π2, about the x-axis.

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Chapter 12.1, Problem 107E

Chapter 12.1, Problem 109E

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MyLab Math with Pearson eText -- 24 Month Access -- for Calculus with Integrated Review

Ch. 12.1 - Identify the graph generated by the parametric...Ch. 12.1 - Prob. 2QC Ch. 12.1 - Prob. 3QC Ch. 12.1 - Prob. 4QC Ch. 12.1 - Prob. 5QC Ch. 12.1 - Prob. 6QC Ch. 12.1 - Explain how a pair of parametric equations...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E

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The surface area of the curve x = cos 3 t , y = sin 3 t , for 0 ≤ t ≤ π 2 , about the x -axis.

Solution Summary: The author calculates the surface area of the curve with the parametric equation x=mathrmcos3t, y=

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The surface area of the curve x=cos3t,y=sin3t, for 0≤t≤π2, about the x-axis.

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