Explanation Given data: The given curve equation is x = ( y 3 / 12 ) + ( 1 / y ) (1) The range of y is 1 ≤ y ≤ 2 . Formula used: Write the expression for length of the curve x = g ( y ) , c ≤ y ≤ d . L = ∫ c d 1 + ( d x d y ) 2 d y (2) Calculation: Differentiate equation (1) with respect to y as follows: d x d y = d d y [ ( y 3 / 12 ) + ( 1 / y ) ] = ( 1 12 ) ( 3 ) y [ 3 − 1 ] − 1 y 2 = 1 4 y 2 − 1 y 2 Find the value of ( d x d y ) 2 . ( d x d y ) 2 = [ 1 4 y 2 − 1 y 2 ] 2 = ( 1 4 y 2 ) 2 + ( 1 y 2 ) 2 − 2 ( 1 4 y 2 ) ( 1 y 2 ) = 1 16 y 4 + 1 y 4 − 1 2 Substitute 1 16 y 4 + 1 y 4 − 1 2 for ( d x d y ) 2 , 1 for c and 2 for d in equation (2) to find the length of the curve

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Chapter 10, Problem 16PE

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Determine the length of the curve x=(y3/12)+(1/y), 1≤y≤2.

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Ch. 10.1 - Finding Cartesian from Parametric...Ch. 10.1 - Finding Cartesian from Parametric...Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Finding Cartesian from Parametric...Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Finding Cartesian from Parametric...

Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Prob. 12E Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Prob. 14E Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Finding Cartesian from Parametric...Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - In Exercises 19–24, match the parametric equations...Ch. 10.1 - In Exercises 19–24, match the parametric equations...Ch. 10.1 - In Exercises 19–24, match the parametric equations...Ch. 10.1 - In Exercises 19–24, match the parametric equations...Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - In Exercises 25–28, use the given graphs of x =...Ch. 10.1 - Finding Parametric Equations Find parametric...Ch. 10.1 - Find parametric equations and a parameter interval...Ch. 10.1 - Prob. 31E Ch. 10.1 - In Exercises 31–36, find a parametrization for the...Ch. 10.1 - 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Chapter 10 Solutions