Explanation Given information: The function f ( x ) have a revolution about the x-axis for the given function and interval: f ( x ) = cos x sin x , [ 0 , π 2 ] Concept used: If f is continuous and f ( x ) ≥ 0 on [ a , b ] , then the solid obtained by rotating the region under the graph about the x-axis has the volume: V = π ∫ a b R 2 d x = π ∫ a b [ f ( x ) ] 2 d x Substitution method of integration : This formula is used to transform one integral into another integral and that integral will be easy to calculate. Identity of sine function: sin 2 x = 2 sin x cos x 1 2 sin 2 x = sin x cos x Calculation: Put the value of f ( x ) in given formula and solve the function: V = π ∫ a b [ f ( x ) ] 2 d x V = π ∫ 0 π 2 [ cos x sin x ] 2 d x V = π ∫ 0 π 2 [ cos x sin x ] d x V = π ∫ 0 π 2 [ 1 2 sin 2 x ] d x Assume that 2 x = u

Loose-leaf Version For Calculus: Early Transcendentals

4th Edition

ISBN: 9781319055912

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 6.3, Problem 14E

To determine

Calculate the volume of revolution about x -axis for the function and interval

f(x)=cosxsinx, [0,π2].

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Chapter 6.3, Problem 13E

Chapter 6.3, Problem 15E

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Chapter 6 Solutions

Loose-leaf Version For Calculus: Early Transcendentals

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Calculate the volume of revolution about x -axis for the function and interval f ( x ) = cos x sin x , [ 0 , π 2 ] .

Solution Summary: The author calculates the volume of revolution about the x-axis for the function and interval f(x)=sqrtmathrmcosx

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Calculate the volume of revolution about x -axis for the function and interval

f(x)=cosxsinx, [0,π2].

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Chapter 6 Solutions

Calculate the volume of revolution about x -axis for the function and interval f ( x ) = cos x sin x , [ 0 , π 2 ] .

Solution Summary: The author calculates the volume of revolution about the x-axis for the function and interval f(x)=sqrtmathrmcosx

Concept explainers

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Calculate the volume of revolution about x -axis for the function and interval f(x)=cosxsinx, [0,π2].

Want to see the full answer?

Chapter 6 Solutions

Calculate the volume of revolution about x -axis for the function and interval

f(x)=cosxsinx, [0,π2].