(e) Give one example where the Green theorem fails, and explain how.
Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help with (c)
Transcribed Image Text:Green's Theorem
(a) State the Green theorem in the plane.
(b) Express part (a) in vector notation.
(c) Give one example where the Green theorem fails, and explain how.
(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, gi(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+z²j and a triangle
bounded by the lines a + y = 1 and -x + y = 1 and y = 0.
(Hint: all the conditions in the Green theorem must be verified.)
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