To compute the flux ∮ F → . n ^ d s of F → ( x , y ) = 〈 x y 2 + 2 x , x 2 y − 2 y 〉 across the simple closed curve that is the boundary of the half disc given by x 2 + y 2 ≤ 3 and y ≥ 0 using vector form of Green’s theorem.

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Answer 1

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Chapter 18.1, Problem 39E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 x y^{2} + 2 x, x^{2} y - 2 y 〉$ across the simple closed curve that is the boundary of the half disc given by $x^{2} + y^{2} \leq 3$ and $y \geq 0$ using vector form of Green’s theorem.

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Answer 2

Question

Chapter 18.1, Problem 39E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 x y^{2} + 2 x, x^{2} y - 2 y 〉$ across the simple closed curve that is the boundary of the half disc given by $x^{2} + y^{2} \leq 3$ and $y \geq 0$ using vector form of Green’s theorem.

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Answer 3

Question

Chapter 18.1, Problem 39E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 x y^{2} + 2 x, x^{2} y - 2 y 〉$ across the simple closed curve that is the boundary of the half disc given by $x^{2} + y^{2} \leq 3$ and $y \geq 0$ using vector form of Green’s theorem.

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Answer 4

Question

Chapter 18.1, Problem 39E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 x y^{2} + 2 x, x^{2} y - 2 y 〉$ across the simple closed curve that is the boundary of the half disc given by $x^{2} + y^{2} \leq 3$ and $y \geq 0$ using vector form of Green’s theorem.

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Answer 5

Chapter 18.1, Problem 39E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 x y^{2} + 2 x, x^{2} y - 2 y 〉$ across the simple closed curve that is the boundary of the half disc given by $x^{2} + y^{2} \leq 3$ and $y \geq 0$ using vector form of Green’s theorem.

Answer 6

Chapter 18.1, Problem 39E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 x y^{2} + 2 x, x^{2} y - 2 y 〉$ across the simple closed curve that is the boundary of the half disc given by $x^{2} + y^{2} \leq 3$ and $y \geq 0$ using vector form of Green’s theorem.

Answer 7

Chapter 18.1, Problem 39E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 x y^{2} + 2 x, x^{2} y - 2 y 〉$ across the simple closed curve that is the boundary of the half disc given by $x^{2} + y^{2} \leq 3$ and $y \geq 0$ using vector form of Green’s theorem.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 18.1 - Prob. 1PQ Ch. 18.1 - Prob. 2PQ Ch. 18.1 - Prob. 3PQ Ch. 18.1 - Prob. 4PQ 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 Ch. 18.1 - Prob. 6E

To compute the flux ∮ F → . n ^ d s of F → ( x , y ) = 〈 x y 2 + 2 x , x 2 y − 2 y 〉 across the simple closed curve that is the boundary of the half disc given by x 2 + y 2 ≤ 3 and y ≥ 0 using vector form of Green’s theorem.

Solution Summary: The author calculates the flux of a vector field F ( x, y ) = 'flux' of the curve enclosing region D.

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To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 x y^{2} + 2 x, x^{2} y - 2 y 〉$ across the simple closed curve that is the boundary of the half disc given by $x^{2} + y^{2} \leq 3$ and $y \geq 0$ using vector form of Green’s theorem.

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Chapter 18 Solutions

To compute the flux ∮ F → . n ^ d s of F → ( x , y ) = 〈 x y 2 + 2 x , x 2 y − 2 y 〉 across the simple closed curve that is the boundary of the half disc given by x 2 + y 2 ≤ 3 and y ≥ 0 using vector form of Green’s theorem.

Solution Summary: The author calculates the flux of a vector field F ( x, y ) = 'flux' of the curve enclosing region D.

Concept explainers

Videos