Explanation Given: The equation of the curves are y = sin x and y = 1 − sin x with x = π 6 and 5 π 6 . The region R is bounded by these two curves. Let f ( x ) = sin x and g ( x ) = 1 − sin x . The region R is revolving about the x axis. Formula used: The volume of the solid (washer method) is V = ∫ a b π ( f ( x ) 2 − g ( x ) 2 ) d x , where f ( x ) and g ( x ) is mentioned above. Calculation: Let l = f ( x ) 2 − g ( x ) 2 . To obtain the volume of the solid, first calculate the value of l with f ( x ) = sin x and g ( x ) = 1 − sin x as follows, l = ( sin x ) 2 − ( 1 − sin x ) 2 = sin 2 x − 1 − sin 2 x + 2 sin x = 2 sin x − 1 Substitute the value of l = 2 sin x − 1 in the above mentioned formula and take x = π 6 as lower limit and x = 5 π 6 as upper limit to calculate the volume of the solid

Calculus, Single Variable: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780134766850

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 6.4, Problem 56E

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To find: The volume of the solid generated when R is revolved about the x axis.

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Chapter 6.4, Problem 55E

Chapter 6.4, Problem 57E

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Calculus, Single Variable: Early Transcendentals (3rd Edition)

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The volume of the solid generated when R is revolved about the x axis.

Solution Summary: The author calculates the volume of the solid generated when R is revolved about the x axis.

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