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

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - 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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].

Want to see the full answer?

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

Videos

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].