To determine The volume of the solid formed by revolving the region bounded by the graphs. Explanation Given information: y = sin x + sec x y = 0 x = 0 x = π 3 Formula: V = π ∫ a b [ f 2 ( x ) − g 2 ( x ) ] d x log a ( 1 x ) = − log a ( x ) cos 2 ( x ) = 1 + cos ( 2 x ) 2 sin 2 ( x ) = 1 − cos ( 2 x ) 2 ∫ a b sec 2 x d x = [ tan x ] a b ∫ a b cos a x d x = [ sin a x a ] a b ∫ a b tan x d x = [ ln cos ( x ) ] a b ∫ a b x a d x = [ x a + 1 a + 1 ] a b Calculation: Calculate the volume of the solid V formed by rotating between the curves of f ( x ) and g ( x ) about x axis using the formula: V = π ∫ a b [ f 2 ( x ) − g 2 ( x ) ] d x Substitute 0 for g ( x ) and sin x + sec x for f ( x ) . V = π ∫ a b [ ( sin x + sec x ) 2 − 0 ] d x = π ∫ a b [ sin 2 x + sec 2 x − 2 sin x sec x ] d x Substitute 0 for a and π 3 for b. V = π ∫ 0 π / 3 [ sin 2 x + sec 2 x − 2 sin x 1 cos x ] d x = π ( ∫ 0 π / 3 sin 2 x d x + ∫ 0 π / 3 sec 2 x d x − 2 ∫ 0 π / 3 tan x d x ) Substitute 1 − cos 2 x 2 for sin 2 x

University Calculus: Early Transcendentals (4th Edition)

4th Edition

ISBN: 9780134995540

Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 8.2, Problem 76E

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The volume of the solid formed by revolving the region bounded by the graphs.

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Chapter 8.2, Problem 75E

Chapter 8.2, Problem 77E

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