Explanation Given: y 2 = x + 4 , x = 0 ; δ ( x , y ) = | y | Formula used: M = ∬ R δ ( x , y ) d A M x = ∬ R y δ ( x , y ) d A M y = ∬ R x δ ( x , y ) d A x ¯ = M y M , y ¯ = M x M Calculation: M = ∬ R δ ( x , y ) d A = 2 ∫ − 4 0 ∫ 0 x + 4 | y | d y d x = 2 ∫ − 4 0 ∫ 0 x + 4 y 2 2 d y d x = 2 2 ∫ − 4 0 [ y 2 ] 0 x + 4 d x = ∫ − 4 0 ( x + 4 ) 2 d x = ∫ − 4 0 x + 4 d x = [ x 2 2 + 4 x ] − 4 0 = 8 M x = ∬ R y δ ( x , y ) d A = 2 ∫ − 4 0 ∫ 0 x + 4 y | y | d y d x = 2 ∫ − 4 0 ∫ 0 x + 4 y 2 d y d x = 2 ∫ − 4 0 [ y 3 3 ]

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.5, Problem 26E

To determine

To find: The center of mass of the region bounded by $y^{2} = x + 4, x = 0;$ $δ (x, y) = | y |$ .

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Chapter 16.5, Problem 25E

Chapter 16.5, Problem 27E

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Chapter 16 Solutions

CALCULUS (CLOTH)

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The center of mass of the region bounded by y 2 = x + 4 , x = 0 ; δ ( x , y ) = | y | .

Solution Summary: The author explains the coordinates of center of mass of the region bounded by y 2 = x + 4 ; (x,

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To find: The center of mass of the region bounded by $y^{2} = x + 4, x = 0;$ $δ (x, y) = | y |$ .

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Chapter 16 Solutions

The center of mass of the region bounded by y 2 = x + 4 , x = 0 ; δ ( x , y ) = | y | .

Solution Summary: The author explains the coordinates of center of mass of the region bounded by y 2 = x + 4 ; (x,

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To find: The center of mass of the region bounded by y2=x+4,x=0;δ(x,y)=|y|.

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Chapter 16 Solutions

To find: The center of mass of the region bounded by $y^{2} = x + 4, x = 0;$ $δ (x, y) = | y |$ .