Let C be the counterclockwise boundary of the region enclosed by the x-axis, the line y = x – 2, and the curve Y = Vr. Use Green's Theorem to evaluate p (2? – 2y³) d.x + (y³ – ay) dy.

Q: (d) |// Vx² + y² dV, where P is the region under the cone z = 2 – ry-plane. /x² + y² and above the…

A: Since you have asked for a multiple question, we will solve the first question for you. If you want…

Q: Evaluate ſf, (3x + 4y²) dA where R is the region in the upper half - plane bounded by the circles x²…

A: As the areas are circular thus convert the integral into polar form. Now determine the limits of the…

Q: Evaluate the surface SS₂ xz ds S is the part of the 2x+2y+z=4 that li- the first octant.

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Q: Let C be a simple closed smooth curve in the plane 2x + 2y + z = 2, oriented as shown here. Show…

A: Given, The equation of the curve is 2x+2y+z=2. The closed integral is ∮C2y dx+3zdy-x dz Let…

Q: Verify: Green's theorem in the plane for f(2x-y³) dx-xydy, where C is the boundary of the region…

A: Given information ∫c2x-y3dx-xydy Here, C is the boundary of the region enclosed by the circle…

Q: Use Green's Theorem to evaluate | F nds, where F = (Va+ 5y, 4x + 5y) %3D C is the boundary of the…

A: We have to evaluate the integral ∫CF→·n→ds, where F→=x+5y,4x+5y. Where C is the boundary of the…

Q: c) By using Green's theorem, evaluate $ (In (x²) + xy² – y²) dx + (ev + x²y – 3xy) dy, where C is…

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Q: Use Green's Theorem to evaluate: F.n ds where F = (Vx + 3y, 2x + 3y) and C is the 2x – x2 boundary…

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Q: Find the area of the surface S where S is the cap cut from the paraboloid z = 2– x – y by the cone z…

A: Given that : z=2-x2-y2z=x2+y2 Now, to find the point of intersection , 2-x2-y2=x2+y2Put…

Q: Use Green's Theorem to evaluate F. nds, where F = (Va + 4y, 2æ + 4y) C is the boundary of the region…

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Q: Use Green's Theorem to evaluate F nds, where F = (Va + 6y, 3x + 6y) C is the boundary of the region…

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Q: Let M be the region bounded by the parabola y = r² and the line y = x + 2. %3D 6. y = r +2 5. 2,4)…

A: Given that, The shaded region bounded by the parabola y=x2 and the line y=x+2 is M.   And the region…

Q: Q2// If F = 3i + 2j- 2yk , Evaluate F dv where V is region bounded by the plane y=0,z=0,z=x and the…

A: We have to evaluate those region which is bdd by region, y=0, z=0, z=x and cylinder means…

Q: Evaluate ffS. Vx² + y² dV, where E is the region tha lies inside the cylinder x? + y² = 16 and…

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Q: b. Evaluate the line integral ycos(xy)dx +(xcos(xy)+x)dy where R is the circle x'+y =9 traversed…

A: Solution Given b). ∫y cos(xy)dx+(xcos(xy)+x3) dyevaluate the line integral

Q: Evaluate the line integral xyld x + (x²+y)dy] +. where c is the saruare farmed by the lines

A: Let us consider a line integral ∫CP dx+Qdy then it can be written as  ∫D∫∂Q∂x-∂P∂y dA  Where, P and…

Q: Use Green's Theorem to evaluate C |F.nds, where F = (Va+ 3y, 20 + 3y) C is the boundary of the…

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Q: Let D be the region between the circles x^2 + y^2 = 1 , x^2 + y^2 = 4 and the curves y = e^2x,…

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Q: Consider the PDE Y Urr + x Uyy + Ux – Uy x² + y? In what region of the xy- plane is this PDE…

A: compare the given equation with Auxx+Buxy+Cuyy+Dux+Euy+Fu=G A=y,B=0,C=x,D=1,E=-1 calculate B2-4AC…

Q: The numerical value of f3dA 3dA (where D is the region bounded by lines y=0 and x= 1 and the…

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Q: Use Green's Theorem to evaluate F. ňds, where F = (Va+ 6y, 3z + 6y) C is the boundary of the region…

A: Solving this by green theoram

Q: Let C be the curve of intersection of the paraboloid x² + y² = z and the cylinder x² + (y − 1)² = 1.…

A: For the given curve we have the following vector valued function: R⇀=2cost. 1+sint,…

Q: Let D be the trapezoidal region in the xy-plane bounded by the graphs of x = 0, y = 1, y = x and =…

A: We will solve the problem.

Q: Evaluate fF.ndS, where F-4xi-2y' j+z'k and S is the surface bounding the region x' +y' =4, and the…

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Q: If F = xy?i + yz? j + zx2k, and S is the region bounded by the triangle with vertices (1,0,0),…

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Q: Q2// If F = 3i + 2j - 2yk, Evaluate F dv where V is region bounded by the plane y=0,z=0,z=x and the…

A: Given that F=3i+2j-2yk Then , ∫VF dv =∫∫∫V∇.F dv Thus to find ∇.F ∇.F=∂3∂x+∂2∂y+∂-2y∂z Thus, ∇.F=0

Q: Find c > 0 such that the area of the region enclosed by the parabolas y = x - c² and y = c - z is 1

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Q: O By using Green's theorem, evaluate $ (In (2²) + æy² – y²) dæ + (ev + x²y – 3ry) dy, where C is the…

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Q: Let C be the boundary curve (oriented counterclockwise) of the region D enclosed by y = Vx, x = 9,…

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Q: Find c > 0 such that the area of the region enclosed by the parabolas y = x 450. c and y = c – x² is…

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Q: Use Green's Theorem to evaluate nds, where F = (Va+ 3y, 2a + 3y) C is the boundary of the region…

A: Given Vector field is  F=x+3y, 2x+3y Comparing with F=P,Q, we get  P = x+3y            and…

Q: lad Use Green's theorem to evaluate y² dx + 3xy dy, where c is the boundary of the semi annular…

A: Given Problem:- Use Green's theorem to evaluate ∮cy2dx+3xydy where c is the boundary of the semi…

Q: Let C be the boundary curve counterclockwise of the semidisk x² + y? < 9, y 2 0. Then f.(-2ydx +…

A: A detailed solution is given below.

Q: Evaluate || F.ndS F = xi + yj+(z² –1)k if and o is the curved surface of the cylinder y = \4-x? from…

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Q: Let D be the trapezoidal region in the xy-plane bounded by the graphs of x = 0, y = 1, y = x and y…

A: Here I am attaching image so that you understand each and every step.

Q: Q7. Use Green's theorem to evaluate fy² dx + 3xy dy, where c is the boundary of the semi annular…

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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: Find the points on the surface xy + yz + zx - x- z =0 where the ant pla

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Q: Q7. Use Green's theorem to evaluate y² dx + 3xy dy, where c is the boundary o the semi annular…

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Q: Let D be the region bounded by the parabola y = x2 and the curve y = sin x, and let P represent a…

A: If the input of the function is more than one, such functions are called multivariable functions.…

Q: 29. Let C be a simple closed smooth curve in the plane 2x + 2y + z = 2, oriented as shown here. Show…

A: Given:

Q: Use Green's Theorem to evaluate Fnds, where F = (VI + 6y, 3x + 6y) C is the boundary of the region…

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Q: Let M be the region bounded by the parabola y = x² and the line y = x +2. %3D 6. y = r + 2 5. 4.…

A: Consider the given information and diagram: Let y=x2 and the line is y=x+2.

Q: Evaluate ſ. (3x² + y)dx + 4y²dy, where C is the boundary of the region in the first quadrant by y =…

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Q: 2. Let D = {(x, y)| x² < y < x + 1, 0 <x < 1}. Let C be the boundary of D with the clockwise…

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Q: 3. Use Greens theorem to evaluate (e* + y²)dx + (e' + x²) dy where c is the boundary of the region…

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Q: Evaluate y dx+3xy dy, where C is the boundary of the semiannual region D in the upper half-plane…

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Q: Use Green's Theorem to evaluate: F n ds where F = (VI+ 5y, 3x + 5y) and C is the boundary of the…

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