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Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and curve C. = (4x + ex sin y)i + (5x + ex cos y sy)j C: The right-hand loop of the lemniscate r² = cos 20 Describe the given region using polar coordinates. Choose 0-values between - and . <0< ≤rs √cos (20) (Type exact answers.) The outward flux is. (Type an integer or a simplified fraction.) The counterclockwise circulation is (Type an integer or a simplified fraction.)

Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and curve C. = (4x + ex sin y)i + (5x + ex cos y sy)j C: The right-hand loop of the lemniscate r² = cos 20 Describe the given region using polar coordinates. Choose 0-values between - and . <0< ≤rs √cos (20) (Type exact answers.) The outward flux is. (Type an integer or a simplified fraction.) The counterclockwise circulation is (Type an integer or a simplified fraction.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and curve C. F= (4x + ex siny)i + (5x + ex cos y sy)j C: The right-hand loop of the lemniscate r² = cos 20 Describe the given region using polar coordinates. Choose 0-values between - and . <0< ≤r≤√cos (20) (Type exact answers.) The outward flux is. (Type an integer or a simplified fraction.) The counterclockwise circulation is. (Type an integer or a simplified fraction.)
Transcribed Image Text:Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and curve C. F= (4x + ex siny)i + (5x + ex cos y sy)j C: The right-hand loop of the lemniscate r² = cos 20 Describe the given region using polar coordinates. Choose 0-values between - and . <0< ≤r≤√cos (20) (Type exact answers.) The outward flux is. (Type an integer or a simplified fraction.) The counterclockwise circulation is. (Type an integer or a simplified fraction.)
Verify the conclusion of Green's Theorem by evaluating both sides of each of the two forms of Green's Theorem for the field F = -3yi + 3xj. Take the domains of integration in each case to be the disk R: x² + y² ≤a² and its bounding circle C: r = (a cos t)i + (a sin t)j, 0≤t≤ 2π. Click the icon to view the two forms of Green's Theorem. The flux is (Type an exact answer, using as needed.) The circulation is. (Type an exact answer, using as needed.)
Transcribed Image Text:Verify the conclusion of Green's Theorem by evaluating both sides of each of the two forms of Green's Theorem for the field F = -3yi + 3xj. Take the domains of integration in each case to be the disk R: x² + y² ≤a² and its bounding circle C: r = (a cos t)i + (a sin t)j, 0≤t≤ 2π. Click the icon to view the two forms of Green's Theorem. The flux is (Type an exact answer, using as needed.) The circulation is. (Type an exact answer, using as needed.)
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