a)State the Green theorem in the plane (d) Prove part (a) assuming that the domain D enclosed by the simple closed curveC with positive orientation is of the formD = {(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 trianglebounded by the lines x + y = 1 and -x + y = 1 and y = 0.(Hint: all the conditions in the Green theorem must be verified.)

Here, in the question, a domain D enclosed by the simple closed curve C with positive orientation is…

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

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 4P: 1-6 Sketch the vector field F by drawing a diagram as in figure 3. F(x,y)=(xy)i+xj

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