Compute the integral |(5y + pz2020, ) dx + (19x – e-4ycos(v) sin y) dy over the portion of the circle x² + y² = 4 in the upper half plane.

Q: 5. Verify Green's Theorem for 0(xy +x )dx+(4x-1) dy where Cis shown below by (a) computing the line…

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Q: 2. VI-x² !! 1 dy dx- dz 0 -1V1-x2

A: Change Cartesian coordinate to cylindrical coordinate by using x = r cos(theta) y = r sin(theta) z =…

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: Compute the line integral (х — y) dx + xe x dy, where C is the closed curve consisting of two line…

A: line integration

Q: 8) By using the double integral in polar coordinate, find ,"[S" e-x²+y>dx]dy

A: The double integral in polar coordinates is given by the formula ∬Rf(x,y)dxdy= ∫ab∫g(θ)h(θ)f(rcosθ,…

Q: Use Green’s Theorem to evaluate  ∫ sin 5y dx + 5x dy  around the boundary curve C of the region R,…

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Q: Evaluate the line integral y = x² from (-1, 1) to (1, 1) and the line segment from (1, 1) to (−1,…

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Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

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Q: Use Green's Theorem to evaluate the line integral f(e*c - 2y)dx+(5x+ev* dy, where C is the 15. 2cos:…

A: We need to find integral.

Q: Evaluate the line integral [21r²yzds with respect to s along the 2 curve C : x = t₁ y = t², z =…

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Q: Use Green's Theorem to evaluate the line integral: 2xy dx + 4x² y² dy Where C is the simply…

A: Use formula of Green's theorem to solve this problem.

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: Use Green's Theorem to calculate line integral o sin(x²) dx + (3x – y) dy where C is a right…

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Q: Use Green's theorem to find the line integral of 2x dx – 7x2 dy counterclockwise around the triangle…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 4y dx -…

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Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve 5y³ dx -…

A: We know that , Green's theorem ,  Consider C be a positively oriented  , simple , closed , piecewise…

Q: Find the line integral with respect to arc length (5x + 3y)ds, where C is the line segment in the…

A: Given integral∫C5x+3ydswhere C is the line segment in x-y plane with the end points P(5,0) and…

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

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Q: 5. Evaluate the double integral (2x – y) dA where D is bounded by the circle with the origin as its…

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Q: Express the sum of integrals as an iterated integral in polar coordinates: •2V3 •4+V16-x² x dx dy +…

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Q: Use Green's theorem in order to compute the line integral (2sin z + 3y²) dx + (sin(4®) + 2x³) dy…

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Q: 2. Evaluate fy³ dx-r³ dy, where C is the circle of radius 2 centered at the origin, in the following…

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Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | (3y +…

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Q: Evaluate the triple integral, 2xy dV, where the intergral is bounded by the parabolic cylinders y =…

A: The given triple integral,

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

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Q: Use Green's Theorem to evaluate the line integral. | 2xy dx + (x + y) dy C: boundary of the region…

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Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x - y) dy for the given path. C:…

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Q: Use Green's Theorem to evaluate the line integral. J. 2xy dx + (x + y) dy C: boundary of the region…

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Q: Compute the integral „2020 (5y + x*0 ") dx + (19x – e -e-4yCos(y) sin y) dy over the portion of the…

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Q: Q21 Verify Green's theorem for $. (xy² + x²)dx + (4x – 1)dy where Cis shown in the figure by (a)…

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

A: Solve

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 8y dx…

A: Green's Theorem:- To find the line integral of a function along a closed curve C…

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 6y3…

A: given circle x2+y2=4

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: Line integration by using Greens theorem

Q: Calculate the line integral ∫Cyxdx+dy over the curve y=lnx in the interval 1≤x≤e (Figure 4).

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Q: Calculate the double integral / Rx cos(2x + y) dA where Rl is the region: 0 <x<,0 < y< 6. 2

A: Here we have to find the value of double integral.

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 6y dx…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 7y dx –…

A: To evaluate the integral ∫C7y3dx-7x3dy, identify the values of P, Q, then find its partial…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 7y3 dx…

A: See attached file for a step by step explanation to evaluate the given line integral.

Q: Express the double integral || (x +1)dA, where 2 is the region in the upper half- plane (i.e. y20)…

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Q: 7. Use Green's Theorem to compute the line integral | ry? dx – x² dy, where C is the triangle with…

A: ∫xy2dx - x2dy triangle vertices are (0,0), (2,0), and (2,2)

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 8y dx…

A: Introduction: Green's theorem is one of calculus' four fundamental theorems, all of which are…

Q: Compute the double integral // Vx² + y² dA where D is the part of the first quadrant lying between…

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Q: Use Green's Theorem to evaluate the line integral , 6y² dx + 5x² dy, where Cis the boundary of the…

A: Green's Theorem: ∮C(Pdx+Qdy)=∫∫R∂Q∂x-∂P∂ydA

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. 3y +…

A: We have to solve the given problem by Green's theorem.

Q: Use Green's Theorem to evaluate the line integral along the gi | 4y3 dx - 4x³ dy Cis the circle x2 +…

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Q: 8) consider the region R in the first quadrant(xz0, y2) bounded by x=2y² X=Y²+1 a) set up, but clo…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 2y3 dx…

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