Explanation Given: Let ∮ C 2 F . d r = 3 π , ∮ C 3 F . d r = 4 π and ∂ F 2 ∂ x − ∂ F 1 ∂ y = 9 on the shaded region. The figure is: Formula used: Green’s Theorem for the region between the three circles: ∫ C 1 F d r − ∫ C 2 F d r − ∫ C 3 F d r = ∬ D ( ∂ F 2 ∂ x − ∂ F 1 ∂ y ) d x d y Calculation: We have to find the value of ∮ C 1 F . d r . Green’s Theorem: ∫ C 1 F d r − ∫ C 2 F d r − ∫ C 3 F d r = ∬ D ( ∂ F 2 ∂ x − ∂ F 1 ∂ y ) d x d y … (1) Substitute the value of ∮ C 2 F . d r = 3 π , ∮ C 3 F . d r = 4 π and ∂ F 2 ∂ x − ∂ F 1 ∂ y = 9 in equation (1)...

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Author: Rogawski

Publisher: MAC HIGHER

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Chapter 18.1, Problem 29E

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Use the Green’s Theorem to determine the circulation of $F$ around $C_{1}$ .

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Chapter 18.1, Problem 28E

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Use the Green’s Theorem to determine the circulation of F around C 1 .

Solution Summary: The author explains how to determine the circulation of F around C 1 using the Green's Theorem.

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Use the Green’s Theorem to determine the circulation of $F$ around $C_{1}$ .

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Use the Green’s Theorem to determine the circulation of F around C 1 .

Solution Summary: The author explains how to determine the circulation of F around C 1 using the Green's Theorem.

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Use the Green’s Theorem to determine the circulation of F around C1.

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Chapter 18 Solutions

Use the Green’s Theorem to determine the circulation of $F$ around $C_{1}$ .