To compute the flux ∮ F → . n ^ d s of F → ( x , y ) = 〈 x y , x − y 〉 across the boundary of the square − 1 ≤ x ≤ 1 and − 1 ≤ y ≤ 1 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 $\vec{F} (x, y) = 〈 x y, x - y 〉$ across the boundary of the square $- 1 \leq x \leq 1$ and $- 1 \leq y \leq 1$ using vector form of Green’s theorem.

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1. Find the gradient vector field of f = x² - y², and sketch it.

3. The figure shows a vector field F and two curves C1 and C2. Are the line integrals of F over C1 and C2 positive, negative, or zero? Explain.

Answer 2

Question

Chapter 18.1, Problem 39E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 x y, x - y 〉$ across the boundary of the square $- 1 \leq x \leq 1$ and $- 1 \leq y \leq 1$ 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 $\vec{F} (x, y) = 〈 x y, x - y 〉$ across the boundary of the square $- 1 \leq x \leq 1$ and $- 1 \leq y \leq 1$ 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 $\vec{F} (x, y) = 〈 x y, x - y 〉$ across the boundary of the square $- 1 \leq x \leq 1$ and $- 1 \leq y \leq 1$ 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 $\vec{F} (x, y) = 〈 x y, x - y 〉$ across the boundary of the square $- 1 \leq x \leq 1$ and $- 1 \leq y \leq 1$ 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 $\vec{F} (x, y) = 〈 x y, x - y 〉$ across the boundary of the square $- 1 \leq x \leq 1$ and $- 1 \leq y \leq 1$ 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 $\vec{F} (x, y) = 〈 x y, x - y 〉$ across the boundary of the square $- 1 \leq x \leq 1$ and $- 1 \leq y \leq 1$ using vector form of Green’s theorem.

Answer 8

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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. 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

To compute the flux ∮ F → . n ^ d s of F → ( x , y ) = 〈 x y , x − y 〉 across the boundary of the square − 1 ≤ x ≤ 1 and − 1 ≤ y ≤ 1 using vector form of Green’s theorem.

Solution Summary: The author calculates the flux of a vector field F ( x, y ) using the vector form of Green's Theorem.

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To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 x y, x - y 〉$ across the boundary of the square $- 1 \leq x \leq 1$ and $- 1 \leq y \leq 1$ 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 , x − y 〉 across the boundary of the square − 1 ≤ x ≤ 1 and − 1 ≤ y ≤ 1 using vector form of Green’s theorem.

Solution Summary: The author calculates the flux of a vector field F ( x, y ) using the vector form of Green's Theorem.

Videos