Explanation Given information : y = x 2 , [ 0 , 10 ] . Formula used: The surface area of revolution is given by s u r f a c e a r e a = 2 π ∫ a b y 1 + ( y ' ) 2 d x By reduction formula ∫ sec n x d x = n − 2 n − 1 ∫ sec n − 2 x d x + sec n − 2 x tan x n − 1 By Pythagorean identity tan 2 x = sec 2 x − 1 Calculation: y = x 2 (Given) ⇒ y ' = 2 x 1 + ( y ' ) 2 = 1 + ( 2 x ) 2 = 1 + 4 x 2 The surface area of revolution is given by s u r f a c e a r e a = 2 π ∫ a b y 1 + ( y ' ) 2 d x = 2 π ∫ 0 2 x 2 1 + 4 x 2 d x Let 2 x = tan θ ⇒ d x = sec 2 θ 2 d θ Changing limits: when x = 10 , θ = tan − 1 ( 2 x ) ⇒ θ = tan − 1 ( 20 ) when x = 0 , θ = tan − 1 ( 0 ) ⇒ θ = 0 s u r f a c e a r e a = 2 π sec 2 θ 2 = 2 π 8 ∫ 0 tan − 1 ( 20 ) tan 2 θ 1 + tan 2 θ sec 2 θ d θ = π 4 ∫ 0 tan − 1 ( 20 ) tan 2 θ sec θ sec 2 θ d θ = π 4 ∫ 0 tan − 1 </

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ISBN: 9781319434540

Author: Rogawski

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Chapter 9.2, Problem 42E

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To compute:The surface area of revolution of the curve y=x2 over the interval [0,10] .

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Chapter 9.2, Problem 41E

Chapter 9.2, Problem 43E

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Chapter 9 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

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The surface area of revolution of the curve y = x 2 over the interval [ 0 , 10 ] .

Solution Summary: The author calculates the surface area of revolution of the curve y=x2 over the interval.

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To compute:The surface area of revolution of the curve y=x2 over the interval [0,10] .

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Chapter 9 Solutions