3. Apply Green's Theorem to evaluate the given integrals: a. $. (2x + y²)dx + (2xy + 3y)dy where C is any simple closed curve in the plane for which Green's Theorem holds. b. f. (3y)dx + (2x)dyC is the boundary of 0

Q: 6. Evaluate the integral fF ds, for F = (-y, x, z) and C is the circle a? + y? = 2,2 = 1.

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Q: 4. Use Cauchy's theorem or integral formula to evaluate the integrals. sin z dz b. a.-dz, where C'…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A: Given Data: Let us consider the given data, ∮C 6xy dx +2xy dy  Where C is the rectangle bounded by…

Q: Use Green's Theorem to evaluate the line integral: f. In(1 + y) dr – #, dy where C is triangle with…

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Q: A. State the Fundamental Theorem of Calculus for Line Integrals. B. Suppose that f(x, y, z)…

A: Part(A) FUNDAMENTAL THEOREM OF CALCULUS FOR LINE INTEGRALS: If we have a smooth curve C, given by…

Q: 2. Use Green's theorem in order to compute the line integral P (x – 4)³ dy – y³ dx where is the…

A: We need to compute the given integral using Green's theorem . ∮C(x-4)3dy-y3dx Where is the circle of…

Q: QUESTION 1 Apply Green's Theorem to evaluate the integral. $ (6x + y3) dx + (3xy2 + 5y) dy Hint:…

A: We have to evaluate the line integral using the green’s theorem ∮(6x+3y3)dx+(3xy2+5y)dy

Q: Evaluate the integral [(e' - y)dx + (sin y +x)dy using Green's theorem where C is 16 bounded by y =…

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Q: Compute each of the following line integrals. Cos(e=") ) dx + (x² + y+1) dy, where C is the circler…

A: Given integral is  ∫Cy-ecosex5!dx+x2+yy+1dyWhere C is the circle r=2.

Q: Calculate the line integral of F Enter an exact answer. [F F. dr i = 8x7+ 6x7 along the path C given…

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Q: Evaluate the line integral F. dr where F = (4 sin x, 3 cos y, cz) and C is the path given by r(t) =…

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Q: 3 : F = 2yi + 3xj, 6 = ³x³ + 2xy, and h = y — 4x². Let (a) Find each of the following: F-V6 = Vh=…

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Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. [ (5y +…

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Q: Verify the Green's theorem for the following integral $. sinydx + (x – cosy) dy where curve C is the…

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Q: a) by parametrizing C, b) by using the Fundamental Theorem of Line Integrals.

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Q: Evaluate the line integral F. dr where F = (3 sin x, 3 cos y, 10xz) and C is the path given by r(t)…

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Q: Use Green's Theorem to evaluate the line integral of F = (x², 6x) around the boundary of the…

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Q: .2 Evaluate the line integral xy dx + x-dy, where C is the path going counterclockwise around the…

A: Given, ∮Cxydx+x2dy, Where C is the path going counterclockwise around the boundary of the rectangle…

Q: 1. Consider the lune enclosed between x² + y² = 1 and x² + (y+1)² =2. Show the following using…

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Q: (a) Verify Green's theorem for the line integral f(x−y)dx + (x+y)dy, where C C is the unit square…

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Q: Use Green's Theorem to evaluate the line integral of F (x°, 9x)

A: Given, the line integral of F=x3, 9x around the boundary of the parallelogram in the following…

Q: Use Green's Theorem to evaluate the line integral $ F · dr, where F(x, y) = (x²,x²) and C consists…

A: Green's theorem: ∮CPdx+Qdy=∫∫R∂Q∂x-∂P∂ydxdy