Explanation Given: A multivariable vector field f ( x , y ) = 〈 x 3 + 2 x , y 3 + y 〉 . A circle D given by x 2 + y 2 = 4 . Formula used: As per vector form of Green’s Theorem: ∮ ∂ D F . n d s = ∬ D d i v F d A Calculation: Let us first find the divergence of the given vector field: ⇒ d i v F = 〈 δ δ x , δ δ y 〉 〈 x 3 + 2 x , y 3 + y 〉 ⇒ d i v F = 3 x 2 + 2 + 3 y 2 + 1 = 3 ( x 2 + y 2 ) + 3 ⇒ d i v F = 3 r 2 + 3 Thus, using vector form of Green’s Theorem, we get: ⇒ ∮ ∂ D F . n d s = ∬ D d i v F d A ⇒ ∮ ∂ D F . n d s = ∬ D ( 3 r 2 + 3 ) d A ⇒ ∮ ∂ D F ...

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 18, Problem 15CRE

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The flux $\oint_{\partial D} F . n d s$ of the given function across the given circle using vector form of Green’s Theorem.

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Chapter 18, Problem 14CRE

Chapter 18, Problem 16CRE

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Chapter 18 Solutions

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The flux ∮ ∂ D F . n d s of the given function across the given circle using vector form of Green’s Theorem.

Solution Summary: The author calculates the flux using the vector form of Green's Theorem.

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To compute:

The flux $\oint_{\partial D} F . n d s$ of the given function across the given circle using vector form of Green’s Theorem.

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Chapter 18 Solutions

The flux ∮ ∂ D F . n d s of the given function across the given circle using vector form of Green’s Theorem.

Solution Summary: The author calculates the flux using the vector form of Green's Theorem.

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To compute: The flux ∮∂DF.nds of the given function across the given circle using vector form of Green’s Theorem.

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Chapter 18 Solutions

To compute:

The flux $\oint_{\partial D} F . n d s$ of the given function across the given circle using vector form of Green’s Theorem.