Explanation Given data: x = t 2 2 (1) y = ( 2 t + 1 ) 3 2 3 (2) Formula used: Consider the general formula for length for a ≤ t ≤ b . L = ∫ a b ( d x d t ) 2 + ( d y d t ) 2 d t (3) Calculation: Find d x d t Differentiate with respect to t of equation (1) as follows. d x d t = d d t [ t 2 2 ] = 1 2 ( 2 t ) = t Find d y d t Differentiate with respect to t of equation (2) as follows. d y d t = d d t ( ( 2 t + 1 ) 3 2 3 ) = 1 3 d d t [ ( 2 t + 1 ) 3 2 ] = ( 1 3 ) ( 3 2 ) [ ( 2 t + 1 ) 3 2 − 1 ] = ( 1 3 ) ( 3 2 ) [ ( 2 t + 1 ) 1 2

Pearson eText University Calculus: Early Transcendentals -- Instant Access (Pearson+)

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Chapter 10.2, Problem 27E

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Find the length of the curve x=t2/2, y=(2t+1)3/2/3, 0≤t≤4.

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Chapter 10.2, Problem 26E

Chapter 10.2, Problem 28E

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Chapter 10 Solutions

Pearson eText University Calculus: Early Transcendentals -- Instant Access (Pearson+)

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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Finding Polar Areas Find the areas of the regions...Ch. 10.5 - Prob. 5E Ch. 10.5 - Prob. 6E Ch. 10.5 - Prob. 7E Ch. 10.5 - Prob. 8E Ch. 10.5 - Find the areas of the regions in Exercises...Ch. 10.5 - Find the areas of the regions in Exercises...Ch. 10.5 - Find the areas of the regions in Exercises...Ch. 10.5 - Prob. 12E Ch. 10.5 - Prob. 13E Ch. 10.5 - Prob. 14E Ch. 10.5 - Prob. 15E Ch. 10.5 - Prob. 16E Ch. 10.5 - Find the areas of the regions in Exercises...Ch. 10.5 - Find the areas of the regions in Exercises...Ch. 10.5 - Prob. 19E Ch. 10.5 - Prob. 20E Ch. 10.5 - Find the lengths of the curves in Exercises 2128....Ch. 10.5 - Prob. 22E Ch. 10.5 - Prob. 23E Ch. 10.5 - Prob. 24E Ch. 10.5 - Prob. 25E Ch. 10.5 - Prob. 26E Ch. 10.5 - Find the lengths of the curves in Exercises 2128....Ch. 10.5 - Prob. 28E Ch. 10.5 - Prob. 29E Ch. 10.5 - Prob. 30E Ch. 10.5 - Prob. 31E Ch. 10.5 - Prob. 32E Ch. 10 - Prob. 1GYR Ch. 10 - Prob. 2GYR Ch. 10 - Prob. 3GYR Ch. 10 - Prob. 4GYR Ch. 10 - Prob. 5GYR Ch. 10 - 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Find the length of the curve x = t 2 / 2 , y = ( 2 t + 1 ) 3 / 2 / 3 , 0 ≤ t ≤ 4 .

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Find the length of the curve x=t2/2, y=(2t+1)3/2/3, 0≤t≤4.

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Chapter 10 Solutions