2. Consider the triangle {(x, y)| x, y > 0, 2x + y < 1}. Let C be the boundary of this triangle oriented in the anticlockwise direction. Find y dx + (x² + y) dy (i) using the definition of line integral directly and without using Green's theorem. (ii) using Green's theorem.

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: 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: Use Green's Theorem to evaluate the line integral. cx2 - y?) dx + 5y? dy C: x² + y² = 9 (x² .

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Q: |-4 Evaluate the line integral by two methods: (a) directly and (b) using Green's Theorem. I. $. (x…

A: According to the given information it is required to evaluate the integral:

Q: Use Green's Theorem to evaluate the line integral. dx + (2 + x) dy -y2/2 - 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. 5y +…

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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: Compute the line integral Sc 2.xy dx + x² dy along the following curves. (a) C1 along the circle x2…

A: In given question that is a conservative vector field mean exact integration in which intrgration…

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. 2x + 3y dx + e…

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Q: Use Green's Theorem to evaluate the line integral. (a) | e2a+y dx +e¬Y dy, where C'is the triangle…

A: In the question we have to evaluate integral. NOTE - As per Bartleby's policy we can not solve…

Q: [[(2x + y²) da + 2xy dy], where C is the line segment from (-1,0) to (1, 2) Evaluate in two…

A: The line integral ∫CMdx+Ndy involves the integration over a specific path. In this case, the line…

Q: 4. Use Green's Theorem to evaluate the line integral | 2xydx+ xy'dy, where C is the triangle with…

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Q: Evaluate the line integral / V(ry + xz + yz) · dĩ over the curve F(t) = (t, 2t, 3t) for 0 <t < 4…

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Q: (2) Find the work done by F(x, y) = (2xy³, 4x²y²) moving a particle on the path C where C is the…

A: Formula: Work done W by a force field F on a particle on the path C is: W=∫C F·dr It is given that…

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: Use Green's Theorem to compute the line integral | ry? dx – x² dy, -

A: Here we are going to use Greens theorem to find the line integral. Since, to compute the integral…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 3y3 dx…

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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 calculate the line integral shown in the figure, along the C curve that…

A: Given integral is ∫Cxydx+2x2dy. We have to calculate the given line integral along the C curve that…

Q: Evaluate the line integral by the two following methods. dx + x2 dy Cis counterclockwise around the…

A: The solution is given in the next steps.

Q: Evaluate the line integral (direct method) | (3x– y) dx – x dy , where C consist of the parabola…

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Q: Verify the Green's theorem for integral x²y dx + xy dy, where C is the boundary described…

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Q: 8. Verify Green's Theorem for + (6y – 3y +z) dz + yx°dy where C is shown below by (a) computing the…

A: Let F=Px,yi+Qx,yj be the vector field and C be the boundary of the region D. The Green's theorem…

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

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Q: Evaluate the line integral (direct method) |(3x– y) dx – x dy , where C consist of the parabola y=…

A: Given integral is, ∫C(3x-y)dx-xdy

Q: Consider the line integral xy dx + xy° dy with C the triangle with vertices (0, 0). (1,0), and (1,…

A: Given, the line integral Where C is the triangle with vertices.

Q: Use Green's Theorem to evaluate the line integral ſ (y + e√x) dx + (2x + cos y²) dy, where the given…

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Q: How do I set up the triple integral of the function xy2 -3z, where the solid is bounded by the…

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Q: 4. Use Green's Theorem to evaluate the line integral | 2xydx+ xy*dy, where C is the triangle with…

A: The given triangle C with the vertices (0,0),(1,0) and (1,2) is as as shown below.

Q: |Evaluate the line integral: f.(r² + y) dx + (4x – cos(y)) dy where C is the boundary of the square…

A: According to Greens theorem, the line integral ∮CPdx+Qdy=∬DQx-PydA. BY the extended version of…

Q: Q#4. Is Green's theorem applicable for all types of line integrals? Explain clearly. Use Green's…

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Q: -) Let -y M(x, y) = x2 and N(x, y) = + y? x2 + y? how that ƏN ƏM dx ду ) Show that -y F(x, y) = x² +…

A: Given :-  A vector field for conservative field in the plane ,  ∂N∂x = ∂M∂y To Determine :-  M x,y =…

Q: 3. Find the exact area of the surface resulting from rotating y = v1 + e* from x = 0 to x = 1 about…

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Q: Use Green's Theorem to evaluate the line integral |(y - x)dx + (2x - y)dy Ic

A: Put the value of x and y and then simple integration.

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

A: given circle x2+y2=4

Q: 6. Use Green's Theorem to evaluate the line integral fc 2xy dx + (x² + y²) dy, if C is the ellipse…

A: Let R be simply connected region with a piecewise  smooth boundary  'C'. If functions 'M' and 'N'…

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: Evaluate the line integral by two methods: (a) directly and (b) using Green's Theorem. C is the…

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Q: Use Green's theorem to evaluate the closed line integral: . x²y dx +x'y dy along C between -1 < x< 2…

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Q: Using Green's theorem, convert the line integral §(6y² dx + 2xdy) to a double integral, where C is…

A: Given integral, ∮C6y2dx+2xdy Here C is the boundary of the square with vertices ±2,2 and ±2,-2.…

Q: Use Green's Theorem to evaluate the line integral cos (y) dx + x²sin (y) dy along CoS the positively…

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Q: Evaluate the line integral: f y² dx + x² dy by parameterizing C where the curve C is a square R with…

A: According to the given information, it is required to evaluate the line integral.

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. e5x + 2y dx +…

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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. 2y3 dx…

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Q: 5) Using Green's theorem, convert the line integral f.(6y² dx + 2xdy) to a double integral, where C…

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Q: 3.4.6 Evaluate the line integral [sin y dx + (x- cos y) dy] taken in the anticlockwise sense, where…

A: Green's Theorem States that  Let C be the positively oriented, smooth, and simple closed curve in a…

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

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Q: Use Green's Theorem to evaluate the line integral (y +eva) dx + (2x + cos y²) dy , where x2 and C is…

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