Explanation Given: We are given that f ( x ) = x 2 , g ( x ) = 2 x , x = 2 and x = 4 Formula used: Moment of inertia and integration formula Calculation: Firstly, make the table for the function, f ( x ) = x 2 as follows, x 0 1 2 3 f ( x ) = x 2 0 1 4 9 Plotthese points to sketch the graph of f ( x ) = x 2 . Now, make the table for the function, g ( x ) = 2 x as follows, x 0 1 2 3 g ( x ) = 2 x 1 2 4 8 Plotthese points to sketch the graph of g ( x ) = 2 x . The equation x = 2 and x = 4 aretheequation of the vertical lines. Now, the graph as follows, Total area A = ∫ 2 4 ( x 2 − 2 x ) d x = [ x 3 3 − 2 x log 2 ] 2 4 = 1.354 Moments about the x -axis M x = ∫ 2 4 [ f ( x ) + g ( x ) 2 ] [ f ( x ) − g ( x ) ] d x = ∫ 2 4 ( x 2 + 2 x ) 2 ( x 2 − 2 x ) d x = 1 2 ∫ 2 4 ( x 4 − 2 2 x ) d x = 1 2 [ x 2 5 − 2 2 x log 4 ] 2 4 = 25.28 2 ≈ 12

Bundle: Calculus, 10th + WebAssign Printed Access Card for Larson/Edwards' Calculus, 10th Edition, Multi-Term

10th Edition

ISBN: 9781305718661

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Question

Chapter 8.2, Problem 86E

To determine

To calculate: The centroid of the region bounded by the graphs of f(x)=x2,g(x)=2x,x=2 and x=4

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Chapter 8.2, Problem 85E

Chapter 8.2, Problem 87E

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Chapter 8 Solutions

Bundle: Calculus, 10th + WebAssign Printed Access Card for Larson/Edwards' Calculus, 10th Edition, Multi-Term

Ch. 8.1 - Choosing an Antiderivative In Exercises 3 and 4,...Ch. 8.1 - Choosing an Antiderivative In Exercises 3 and 4,...Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Choosing a Formula In Exercises 514, select the...Ch. 8.1 - Prob. 6E Ch. 8.1 - Choosing a Formula In Exercises 514, select the...Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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The centroid of the region bounded by the graphs of f ( x ) = x 2 , g ( x ) = 2 x , x = 2 and x = 4

Solution Summary: The author explains how to calculate the centroid of the region bounded by the graphs of f(x)=x

To calculate: The centroid of the region bounded by the graphs of f(x)=x2,g(x)=2x,x=2 and x=4

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Chapter 8 Solutions