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ith positive orientation is of the form Dy SII D = {(x,y) | a ≤ y ≤ b, g₁(y) ≤ x ≤ 92(y)}; re g₁(y), 92(y) are continuous functions, and a, b are some y Green's theorem for a vector field F(x,y) = y²i + x nded by the lines x+y=1 and -x+y=1 and y = 0. t: all the conditions in the Green theorem must b

ith positive orientation is of the form Dy SII D = {(x,y) | a ≤ y ≤ b, g₁(y) ≤ x ≤ 92(y)}; re g₁(y), 92(y) are continuous functions, and a, b are some y Green's theorem for a vector field F(x,y) = y²i + x nded by the lines x+y=1 and -x+y=1 and y = 0. t: all the conditions in the Green theorem must b

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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a)State the Green theorem in the plane

(d) Prove part (a) assuming that the domain D enclosed by the simple closed curve C with positive orientation is of the form D = {(x, y) | a ≤ y ≤ b, g₁(y) ≤ x ≤ 9₂(y)}, where gi(y), 92(y) are continuous functions, and a, b are some real numbers. (e) Verify Green's theorem for a vector field F(x, y) = y²i + x²j and a triangle bounded by the lines x + y = 1 and -x + y = 1 and y = 0. (Hint: all the conditions in the Green theorem must be verified.)
Transcribed Image Text:(d) Prove part (a) assuming that the domain D enclosed by the simple closed curve C with positive orientation is of the form D = {(x, y) | a ≤ y ≤ b, g₁(y) ≤ x ≤ 9₂(y)}, where gi(y), 92(y) are continuous functions, and a, b are some real numbers. (e) Verify Green's theorem for a vector field F(x, y) = y²i + x²j and a triangle bounded by the lines x + y = 1 and -x + y = 1 and y = 0. (Hint: all the conditions in the Green theorem must be verified.)
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