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

Thomas' Calculus: Early Transcendentals, Single Variable (14th Edition)

14th Edition

ISBN: 9780134439419

Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher: PEARSON

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Chapter 11.2, Problem 27E

To determine

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

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Chapter 11.2, Problem 26E

Chapter 11.2, Problem 28E

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Chapter 11 Solutions

Thomas' Calculus: Early Transcendentals, Single Variable (14th Edition)

Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Finding Cartesian from Parametric...

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