Explanation Given: A multivariable vector field F ( x , y , z ) = 〈 x y , y z , x 2 z + z 2 〉 . S is the boundary of the box [ 0 , 1 ] × [ 2 , 4 ] × [ 1 , 5 ] . Formula used: Using Gauss Divergence Theorem, ∬ S F . d S = ∭ V d i v F d V Calculation: Let us first find the divergence of the given vector field: ⇒ d i v F = 〈 δ δ x , δ δ y , δ δ z 〉 ⋅ 〈 x y , y z , x 2 z + z 2 〉 ⇒ d i v F = δ δ x ( x y ) + δ δ y ( y z ) + δ δ z ( x 2 z + z 2 ) ⇒ d i v F = y + z + x 2 + 2 z = x 2 + y + 2 z Upon using Divergence Theorem we can set up the triple integral as: ⇒ ∬ S F ...

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Author: Rogawski

Publisher: MAC HIGHER

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Chapter 18, Problem 23CRE

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The surface integral $\iint_{S} F . d S$ using Divergence Theorem.

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Chapter 18, Problem 22CRE

Chapter 18, Problem 24CRE

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Chapter 18 Solutions

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The surface integral ∬ S F . d S using Divergence Theorem.

Solution Summary: The author calculates the surface integral S F using the Gauss Divergence Theorem.

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To compute:

The surface integral $\iint_{S} F . d S$ using Divergence Theorem.

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Chapter 18 Solutions

The surface integral ∬ S F . d S using Divergence Theorem.

Solution Summary: The author calculates the surface integral S F using the Gauss Divergence Theorem.

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To compute: The surface integral ∬SF.dS using Divergence Theorem.

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Chapter 18 Solutions

To compute:

The surface integral $\iint_{S} F . d S$ using Divergence Theorem.