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Using Green's theorems, compute the circulation and flux of the following vector fields: a) F(x, y) = (x + y)i - (x² + y²)j around and across the triangle bounded by y = 0, x = 1 and y = x. b) F(x, y) = (x + 3y)i + (2x - y)j around and across the ellipse given by x² + 2y² = 2. arctan (y/x)i + ln(x² + y²)j around and across the boundary of the region defined by 1 ≤r ≤ 2 and 0 ≤ ≤ in polar coordinates. c) F(x, y) =

Using Green's theorems, compute the circulation and flux of the following vector fields: a) F(x, y) = (x + y)i - (x² + y²)j around and across the triangle bounded by y = 0, x = 1 and y = x. b) F(x, y) = (x + 3y)i + (2x - y)j around and across the ellipse given by x² + 2y² = 2. arctan (y/x)i + ln(x² + y²)j around and across the boundary of the region defined by 1 ≤r ≤ 2 and 0 ≤ ≤ in polar coordinates. c) F(x, y) =

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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Can someone please solve part c.)?

Using Green's theorems, compute the circulation and flux of the following vector fields: a) F(x, y) = (x + y)i - (x² + y²)j around and across the triangle bounded by y = 0, x = 1 and y = x. b) F(x, y) = (x + 3y)i + (2x - y)j around and across the ellipse given by x² + 2y² = 2. arctan(y/x)i + ln(x² + y²)j around and across the boundary of the region defined by 1 ≤r ≤ 2 and 0 ≤ ≤ in polar coordinates. c) F(x, y) =
Transcribed Image Text:Using Green's theorems, compute the circulation and flux of the following vector fields: a) F(x, y) = (x + y)i - (x² + y²)j around and across the triangle bounded by y = 0, x = 1 and y = x. b) F(x, y) = (x + 3y)i + (2x - y)j around and across the ellipse given by x² + 2y² = 2. arctan(y/x)i + ln(x² + y²)j around and across the boundary of the region defined by 1 ≤r ≤ 2 and 0 ≤ ≤ in polar coordinates. c) F(x, y) =
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