Use Green's Theorem to evaluate nds, where F = (Va+ 6y, 3x + 6y) C is the boundary of the region enclosed by y = lx x and the x-axis (oriented positively).

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 the integral e5xy dA, 2 where R is the region enclosed by the lines y = 3x, y = x, y =, y…

A: Given Region R is Enclosed by : y=3x,y=x,y=1x, y=2x  ⇒yx=3, yx=1, xy=1, xy=2 Let yx=2 , xy=2 1≤u≤3,…

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: Use Green's Theorem to evaluate: So F.ñ ds C where F = (Vx + 6y, 2x + 6y) and C is the boundary of…

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Q: Evaluate Slo I –dA, y3(x3+1) where D is the region bounded by x = -y³, х%3D 3 аnd the x — аxis. |

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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: Use Green's Theorem to evaluate the line integral. |v² dx + xy dy C: boundary of the region lying…

A: Introduction: The line integral ∫CF·dr geometrically represents the circulation of the function F…

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: Evaluate the double integral |xcosy dA: where R is the triangular region R bounded by the lines y =…

A: To evaluate the integral, first identify the limits of x and y from the region of integration and…

Q: Evaluate || xdA, where R is the finite region bounded by the axes and 2y +x = 2. R

A: Given: I=∫∫RxdA And 2y+x=2⇒y=1-x2 We know that; ∬dA=∬dydx or ∬dxdy   Now find the x & y…

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: Use Green's Theorem to evaluate: F dr x² and the where F = (Va +6y, 4x + 6y) and C is the boundary…

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Q: Evaluate using Green's Theorem ф худх + (х + уjdy Where C is the boundary of the region between x? +…

A: From Green's theorem:   ∮F1dx+F2dy=∬∂F2∂x-∂F1∂ydxdy   Given:   I=∮xydx+x+ydy   F1=xy⇒∂F1∂y=∂…

Q: Evaluate the integral ∭U(x4+2x2y2+y4)dxdydz, where the region U is bounded by the surface x2+y2≤1…

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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: (c) By using the Green's theorem, evaluate $(2xy) dx + (4x²y*) dy if C is the boundary of a region…

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Q: Use Green's Theorem to evaluate n ds, where F = (Va + 5y, 4x + 5y) and C is the boundary of the…

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Q: express the intergral ∫∫2x dA, as iterated intergral, where R is the region bounded by y=x+12 and…

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Q: Use Green's Theorem to evaluate: • dr C where F = (Vx + 3y, 2x + 3y) and C is the boundary of the…

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Q: Use Green's Theorem to evaluate f x2 dx+ (xy+y²) dy where C is the boundary of the region R bounded…

A: follow next step

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: Q3 Verify Green's theorem in plane for (x² - 2xy) dx + (x²y + 3)dy where c is the boundary of the…

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Q: 3. Use the substititutions u = y – x, and v = y +2x to evaluate the integral (2x +y)(x – y) dx dy…

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Q: Let R be a region bounded by the four planes a = 0. y = 0, z= 0 and æ + y+z=2. Evaluate SSS 24x dV…

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Q: Evaluate SSS z²dV, where R is the region given. R by above the plane Z=0 and between the sphenes + 2…

A: In spherical coordinates,                                             So,

Q: (b) Evaluate || (x²y³ – xy) dA over the region R enclosed between 7 and y = 1 x =5y,x := v9x, y =

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

Q: 2. Calculate the double integral 2ry dA, where R is the triangular region with vertices (0,0), R (1,…

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Q: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

A: Given problem:-

Q: Evaluate . (y² z)dV where E be the region in the first octant E bounded by the planes x = z, x + z =…

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Q: Use Green's Theorem to evaluate |F.n ds, where F (Va + 4y, 2x + 4y) 2x x2 and the x-axis (oriented…

A: Given F→=x+4y,2x+4y We have to find the ∫CF→⋅n→ds, where C is the boundary of the region enclosed by…

Q: Let f(x,y)=|x|+sin (2x−3y). If R is the region bounded by the quadrilateral of vertices (0,3),…

A: We have to find the given integral according to the given region

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

A: Greens theorem if u(x,y) and v(x,y) are continuous functions of x and y ;∮  u dx + v dy = ∬(∂v∂x -…

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

A: Given information is: Vector field :

Q: Use Green's Theorem to calculate S,x²y³dx + (xy – y²)dy where C is the boundary of the region lying…

A: Greens Theorem:

Q: Use an appropriate transformation to evaluate the integral [[(x+2y)(x-y)' dxdy for the R region R…

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Q: On the x,y – plane, R is the region bounded by y=-Vx, y=-2/x, x=1, and x=4. (a) Sketch the region R.…

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Q: Evaluate the moment My and My of the region bounded by y = 2x + 1, x + y = 7 and x = 8.

A: evaluate the moment Mx and My of the region bounded by y=2x+1 , x+y=7 , x=8

Q: Find the volume of the region W bounded by x² + y² = 1, z=1-2²-y², and z=1+z²+y².

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Q: Use Green's Theorem to evaluate the line integral $. (x2-y2)dx + (2y -x)dy where C consists of the…

A: We will plot the region bounded by two given curves and find the integral using Greens theorem

Q: 21 Verify that (y² – 2x )dx +(2xy +x²)dy = || dA where C is the boundary of a region ôy -. R R…

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Q: Let D be the region in the xy-plane bounded by x2 + y² = 1 and x2 +y2 = 4, %3D Evaluate S Spf (x, y)…

A: Double integration

Q: : Evaluate ff,(x + 2y)dA, where D is the region in space bounded by y 2x and y = 1+ x2.

A: The given region D is bounded by the curvesy=2x2 and y=1+x2.We will find first the point of…

Q: b. Let C be the boundary of the region D = {(x,y) | 1 x dv

A: That's easy. Have a great day!!!

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

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Q: compute the area of ∫ D∫4xy-y3dA when D is the region bounded by y = √x and y=x3

A: Given  The given integral is ∫D∫4xy-y3dA. Region bounded by y=x and y=x3. Apply formula…

Q: Verify Green’s Theorem for F⃗ = , where C is the boundary of the region bounded by x = 0 , y = 0 ,…

A: Given that F=3x2-8y2,4y-6xy bounded by x=0,y=0,x+y=1Verify green's theoremGreens theorem is∫C…

Q: 3. Let R be the region bounded by the lines r+ y = 0, x – y = 0, and y = 2. Evaluate the double…

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Q: Let D = {(z, ) | 2<r < 3, -Ses 0). Sketch the region D, and evaluate the double integral n -4y dA.

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Q: Verify that [y- 2x )dx +(2xy +x²)dy = dA where C is the boundary of a region %3D R R defined by y=0,…

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Q: Verify Green's theorem in a plane | (xy +x²)dx + x² dy, where C is the boundary of the region formed…

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