Explanation Given information: The curve is f ( x ) = x 3 2 − 1 3 x 1 2 on [ 4 , 16 ] . Formula used: The length of the arc of the curve f ( x ) on [ a , b ] is given by s = ∫ a b 1 + [ f ' ( x ) ] 2 d x Calculation: f ( x ) = x 3 2 − 1 3 x 1 2 on [ 4 , 16 ] (Given) Differentiating f ( x ) = x 3 2 − 1 3 x 1 2 with respect to ‘x’, we get f ' ( x ) = 3 2 ( x 1 2 ) − 1 6 ( x − 1 2 ) = 3 2 ( x ) − 1 6 x = ( 9 x − 1 6 x ) ⇒ [ f ' ( x ) ] 2 = ( 9 x − 1 6 x ) 2 The length of the arc of the curve f ( x ) = x 3 2 − 1 3 x 1 2 on [ 4 , 16 ] is given by s = ∫ 4 16 1 + [ f ' ( x ) ] 2 d x = ∫ 4 16 1 + ( 9 x − 1 6 x <

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 6.4, Problem 18PS

To determine

To find:The length of the arc of the curve f(x)=x32−13x12 on [4,16] .

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Chapter 6.4, Problem 17PS

Chapter 6.4, Problem 19PS

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Chapter 6 Solutions

Calculus

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The length of the arc of the curve f ( x ) = x 3 2 − 1 3 x 1 2 on [ 4 , 16 ] .

Solution Summary: The formula used to find the length of the arc of a curve is 56.67 units.

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To find:The length of the arc of the curve f(x)=x32−13x12 on [4,16] .

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Chapter 6 Solutions