Explanation Given: The value of surface integral ∬ ∂ W 〈 x + x y + z , x + 3 y − 1 2 y 2 , 4 z 〉 ⋅ d S = 16 . The surface S any closed smooth surface. Formula used: Divergence Theorem, ∬ S F ⋅ d S = ∭ E d i v F d V Calculation: Let us first find the divergence of the given vector field. ⇒ F ( x , y , z ) = 〈 x + x y + z , x + 3 y − 1 2 y 2 , 4 z 〉 ⇒ d i v F = 〈 ∂ ∂ x , ∂ ∂ y , ∂ ∂ z 〉 ⋅ 〈 x + x y + z , x + 3 y − 1 2 y 2 , 4 z 〉 ⇒ d i v F = ∂ ∂ x

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 18, Problem 27CRE

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Volume of the region $W$ .

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Chapter 18, Problem 26CRE

Chapter 18, Problem 28CRE

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Ch. 18.1 - Prob. 1PQ Ch. 18.1 - Prob. 2PQ Ch. 18.1 - Prob. 3PQ Ch. 18.1 - Prob. 4PQ Ch. 18.1 - Prob. 5PQ Ch. 18.1 - Prob. 1E Ch. 18.1 - Prob. 2E Ch. 18.1 - Prob. 3E Ch. 18.1 - Prob. 4E Ch. 18.1 - Prob. 5E

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Volume of the region W .

Solution Summary: The author evaluates the volume of the region W using the divergence theorem.

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Volume of the region $W$ .

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Volume of the region W .

Solution Summary: The author evaluates the volume of the region W using the divergence theorem.

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To evaluate: Volume of the region W.

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Chapter 18 Solutions

To evaluate:

Volume of the region $W$ .