Explanation Given: The solid region is defined by x ≥ 0 , y ≥ 0 , x 2 + y 2 ≤ 4 and x ≤ z ≤ 32 − x and the mass density is δ ( x , y , z ) = 6 y g/cm 3 Formula used: The total mass of a region W with a given mass density of δ ( x , y , z ) is the solution of the integration ∭ V δ ( x , y , z ) d V (in 3-dimention) where d V is an elementary volume of the region W . Calculation: Here the region is the given solid, so, 0 ≤ y ≤ 4 − x 2 ; then 0 ≤ x ≤ 2 and x ≤ z ≤ 32 − x So, ∭ V δ ( x , y , z ) d V = ∫ 0 2 ∫ x 32 − x ∫ 0 4 − x 2 6 y d

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 16.5, Problem 6E

To determine

The total mass of a solid region $W$ assuming a mass density of $δ (x, y, z)$

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Chapter 16.5, Problem 5E

Chapter 16.5, Problem 7E

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The total mass of a solid region W assuming a mass density of δ ( x , y , z )

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The total mass of a solid region $W$ assuming a mass density of $δ (x, y, z)$

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The total mass of a solid region W assuming a mass density of δ ( x , y , z )

Solution Summary: The author explains the formula used to determine the total mass of a solid region W.

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The total mass of a solid region W assuming a mass density of δ(x,y,z)

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The total mass of a solid region $W$ assuming a mass density of $δ (x, y, z)$