To compute the flux ∮ F → . n ^ d s of F → ( x , y ) = 〈 cos y , sin y 〉 across the boundary of the square 0 ≤ x ≤ 2 and 0 ≤ y ≤ π 2 using vector form of Green’s theorem.

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Chapter 18.1, Problem 42E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 \cos y, \sin y 〉$ across the boundary of the square $0 \leq x \leq 2$ and $0 \leq y \leq \frac{π}{2}$ using vector form of Green’s theorem.

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Compute the flux ∫F · n ds of F across the curve C for the given vector field and curve using the vector form of Green’sTheorem. F(x, y) =〈xy,x − y〉across the boundary of the square −1 ≤ x ≤ 1, −1 ≤ y ≤ 1

Answer 2

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Chapter 18.1, Problem 42E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 \cos y, \sin y 〉$ across the boundary of the square $0 \leq x \leq 2$ and $0 \leq y \leq \frac{π}{2}$ using vector form of Green’s theorem.

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Answer 3

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Chapter 18.1, Problem 42E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 \cos y, \sin y 〉$ across the boundary of the square $0 \leq x \leq 2$ and $0 \leq y \leq \frac{π}{2}$ using vector form of Green’s theorem.

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Answer 4

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Chapter 18.1, Problem 42E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 \cos y, \sin y 〉$ across the boundary of the square $0 \leq x \leq 2$ and $0 \leq y \leq \frac{π}{2}$ using vector form of Green’s theorem.

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Answer 5

Chapter 18.1, Problem 42E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 \cos y, \sin y 〉$ across the boundary of the square $0 \leq x \leq 2$ and $0 \leq y \leq \frac{π}{2}$ using vector form of Green’s theorem.

Answer 6

Chapter 18.1, Problem 42E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 \cos y, \sin y 〉$ across the boundary of the square $0 \leq x \leq 2$ and $0 \leq y \leq \frac{π}{2}$ using vector form of Green’s theorem.

Answer 7

Chapter 18.1, Problem 42E

To determine

To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 \cos y, \sin y 〉$ across the boundary of the square $0 \leq x \leq 2$ and $0 \leq y \leq \frac{π}{2}$ 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 ) = 〈 cos y , sin y 〉 across the boundary of the square 0 ≤ x ≤ 2 and 0 ≤ y ≤ π 2 using vector form of Green’s theorem.

Solution Summary: The author calculates the flux of F ( x, y ) = cos, sin, and a curve enclosing region D.

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To compute the flux $\oint \vec{F} . \hat{n} d s$ of $\vec{F} (x, y) = 〈 \cos y, \sin y 〉$ across the boundary of the square $0 \leq x \leq 2$ and $0 \leq y \leq \frac{π}{2}$ 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 ) = 〈 cos y , sin y 〉 across the boundary of the square 0 ≤ x ≤ 2 and 0 ≤ y ≤ π 2 using vector form of Green’s theorem.

Solution Summary: The author calculates the flux of F ( x, y ) = cos, sin, and a curve enclosing region D.

Concept explainers

Videos