Use Green's Theorem to evaluate the integral o (3x - y)dx + 4xdy where C is the circle x +y? = 1 oriented counterclockwise. NOTE: Enter the exact answer. (3x² - – y)dx + 4xdy =

Q: Find the integral surface of the linear PDE xp - yq = z which contains the circle x² + y? = 1, z=1.

A: From Lagrange method

Q: Use Green's Theorem to evaluate the line integral ∫c ( x − y ) dx + ( x + y ) dy where C is the…

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Q: Evaluate the line integral 2 Cx2y)dx- 2xdy along each of the following closed paths, taken…

A: Given that the integral,

Q: Apply Green's Theorem to evaluate the integral. $(7y + x)dx + (y + 9x)dy C: The circle (x-3)² +…

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Q: Use Green's theorem to evaluate line integral (9y – In(x2 + y2)) dx + (2 arctan( (2)) dy, where C is…

A: Green's theorem defines that : for ∮CPdx-Qdy there is an integral exists of ∫D∫∂Q∂X-∂P∂Y.dA Here,…

Q: Let C be the positively oriented circle x? + y? = 1. Use Green's Theorem to evaluate the line…

A: Compare the integral ∫C19ydx+20xdy with ∫CMdx+Ndy to obtain M=19yN=20x Consider…

Q: Apply Green's Theorem to evaluate the integral. (8y + x)dx + (y + 3x)dy C: The circle (x - 9)² + (y…

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Q: Can you show the steps on how to do this integral?

A: Consider the provided question, (3) Evaluate the integral by using the greens theorem,

Q: Evaluate the integral ∫C xy2ds, where C is the part of the unit circle x2+y2=4 in the first…

A: Use parametric to solve this

Q: Apply Green's Theorem to evaluate the integral. P(7y + x)dx + (y + 9x)dy C: The circle (x- 1)² + (y…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. ∫C…

A: by usingGreen's Theorem to evaluate the line integral along the given positively oriented curve.…

Q: How do I evaluate this?

A: Let C be the quarter circle centered at (2,0) that goes from (1,0) to (2,1).

Q: Use polar coordinates to find the integral 16 - x² - y? dx dy where R is the circle x? + y? < 4.

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Q: Evaluate the integral: I = S, dz where C is the circle |z|=1. O (A) I = –27ni. O (B) I = -3Ti. O (C)…

A: By using Cauchy integral Formula-

Q: Use Green's Theorem to evaluate the integral (x² - y)dax + 3xdy where C is the circle x² + y² = 1…

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Q: 3. Evaluate the integral: I = J dz where C is the circle |z|=1. O (A) I O (B) I =-3i. O (C) I =…

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Q: Evaluate the integral į. I. (1 - x - x² – y²)dA Where R is one-unit circle on the xy-plane.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Evaluate the line integral g. y³ dx – x²dy, where C is the positively oriented circle of radius 2…

A: Solved below.

Q: Apply Green's Theorem to evaluate the integral. fror- C: The circle (x - 5)2 + (y – 1)2 = 8 x)dx +…

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Q: Let M(r, y) = y – cos y and N(r, y) = x sin y. Use the Green's Theorem to calculate the line…

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Q: Apply Green's Theorem to evaluate the integral. fror (13y + x)dx + (y + 9x)dy C: The circle (x- 5)?…

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

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Q: (a) Let f(z) = 1 - 2i)(24 – 23) - 2 Using CRT, evaluate the integral Of(2)dz, where the contour C is…

A: 1. The point z=a is said to be an isolated singularity if there exists a number such that f(z) is…

Q: Use Green's Theorem to evaluate the integral (x² – y)dx + 4.xdy where C is the circle x? + y? = 25…

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Q: Apply Green's Theorem to evaluate the integral. (3y + x) dx + (y + 5x)dy C: The circle (x - 2)² +…

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Q: O (x² – y²) dx + x dy where is the circle x + y² = 9.

A: Green's theorem states that ∮CM dx+N dy=∬R∂M∂y-∂M∂ydx dy Here M=x2-y2 and N=x Hence the integral…

Q: Find the integral fc ez dz where C is the circle |z| = 3 in CCD. (z – 1)2(z – 2) %3D -

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Q: Use either form of Green's Theorem to evaluate the following line integral. 03x y dx+ 4x y dy; C is…

A: According to the given information, it is required to find the value of integral using Green’s…

Q: 157. Calculate -x²ydx + xy? dy, where C is a circle of radius 2 centered at the origin and oriented…

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Q: Jse Green's theorem to evaluate $ (2°e* + 4y) dz + (-5x+ y* sin(y)) dy, where C is the…

A: The given path C is circle x2+y2=16. Therefore: D= (x, y) : x2+y2≤16

Q: Let C be the circle x + y = 16 oriented counterclockwise. %3D Use Green's Theorem to evaluate the…

A: Let C be the circle x2+y2=16 oriented counterclockwise. Use Green's theorem to evaluate the…

Q: (a) Let f(z) = %3D (z + 4- i) (z4 + 5z³) Using CRT, evaluate the integral Of(2)dz, where the contour…

A: In the given question we have to evaluate the integral                               where the…

Q: 15. Evaluate the contour integral e3z I (z+ 2)ªdz where C' is the circle |z| = . 9e6 2 O 27 9e-6 O…

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Q: Use Cauchy's Integral formula to evaluate the integral: Sa (z+1) e2z dz where C is a circle |z| = 3.…

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Q: Evaluate the line integral G. dr with G(x, y) = xyi+ 2y² j, and C is the closed path comprising the…

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Q: (3z+1) z'e (b) $1+2 z'e² (a) p- - dz -dz 3 (s + z7)(1– z)z?

A: Evaluate the given two integrals over the circle z=4 (a) Let fz=3z+12zz-12z+5 The singularities of…

Q: 'Evaluate the double integral (3x – y) dA, where R is the region in the first quadrant enclosed by…

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Q: Evaluate the line integral § (x − y) dx + (x + y) dy, where C is the circle with center the origin…

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Q: Let C denote the positively oriented circle z-i=2. Evaluate the integral: 1 dz +4

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Q: Apply Green's Theorem to evaluate the integral. fror- C: The circle (x - 4)² + (y – 1)² = 5 +x)dx +…

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Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

A: Greens theorem

Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

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Q: Let M(x, y) = y - cos y and N(x, y) = x sin y. Use the Green's Theorem to calculate the line…

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Q: #3. Evaluate the line integral O (y dx- x dy) where C is the positively oriented circle with center…

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Q: 3. (a) Use Green's theorem to evaluate the line integral 4 y* dx – a* dy where C is the positively…

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Q: Using Green’s formula, evaluate the line integral ∮C(x−y)dx+ (x+y)dy, where C is the circle…

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Q: Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line…

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Q: Apply Green's Theorem to evaluate the integral. $(8y + x)dx +x)dx + (y + 7x)dy C $(BY+x +x)dx + (y +…

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