1. Verify Green's theorem in the plane for $ (3x2- 8y,dx + (4y - 6xy)dy, where C is the boundary of the region defined by: (a) y = Vx, y = x2; (b) x= 0, y= 0, x+y = 1. Ans. (a) common value = 3/2 (b) common value = 5/3 2. Verify Green's theorem in the plane for (3x + 4y) dx + (2x -- 3y)dy where C, a circle of radius two with center at the origin of the xy plane, is traversed in the positive sense. Ans. - 8TT
1. Verify Green's theorem in the plane for $ (3x2- 8y,dx + (4y - 6xy)dy, where C is the boundary of the region defined by: (a) y = Vx, y = x2; (b) x= 0, y= 0, x+y = 1. Ans. (a) common value = 3/2 (b) common value = 5/3 2. Verify Green's theorem in the plane for (3x + 4y) dx + (2x -- 3y)dy where C, a circle of radius two with center at the origin of the xy plane, is traversed in the positive sense. Ans. - 8TT
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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Transcribed Image Text:1. Verify Green's theorem in the plane for
(3x²- 8y²)dx + (4y – 6xy)dy, where C is the boundary of the
region defined by: (a) y = Vx, y = x²; (b) x= 0, y= 0, x+y = 1.
Ans. (a) common value = 3/2
(b) common value = 5/3
2. Verify Green's thbeorem in the plane for
(3x + 4y)dx + (2x -- 3y)dy where C, a circle of radius two
with center at the origin of the xy plane, is traversed in the positive sense.
Ans. - 87T
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