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Problem 9.1 Green's theorem in the plane 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, z = 1 and y = x. b) F(x, y) = (x+3y)i + (2x - y)j around and across the ellipse given by z² + 2y² = 2. c) F(x, y) = arctan(y/z)i + ln(z² + y²)j around and across the boundary of the region defined by 1

Problem 9.1 Green's theorem in the plane 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, z = 1 and y = x. b) F(x, y) = (x+3y)i + (2x - y)j around and across the ellipse given by z² + 2y² = 2. c) F(x, y) = arctan(y/z)i + ln(z² + y²)j around and across the boundary of the region defined by 1

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.FOM: Focus On Modeling: Vectors Fields
Problem 11P
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Problem 9.1 Green's theorem in the plane 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, z = 1 and y = x. b) F(x, y) = (x+3y)i + (2x - y)j around and across the ellipse given by z² + 2y² = 2. c) F(x, y) = arctan(y/z)i + ln(x² + y2)j around and across the boundary of the region defined by 1 <r < 2 and 0 << in polar coordinates.
Transcribed Image Text:Problem 9.1 Green's theorem in the plane 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, z = 1 and y = x. b) F(x, y) = (x+3y)i + (2x - y)j around and across the ellipse given by z² + 2y² = 2. c) F(x, y) = arctan(y/z)i + ln(x² + y2)j around and across the boundary of the region defined by 1 <r < 2 and 0 << in polar coordinates.
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