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

Q: Q1: Evaluate: 2x dV where E is the region under the plane 2x + 3y + z = 6 that lies in the first…

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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 JJ, xy dA, where D is the region bounded by the curves xy = 2,4y = x² and y = 4. а.

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Q: 4. Evaluate S, cos dA where D is the region bounded by D = {(x, y)/ VL < x < v3Ln , 0 < y< x² }.

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Q: Evaluate p (x² – 2xy)dx + (x²y +3)dy around the boundary of the region defined by y? = 8x and x = 2…

A: To evaluate : ∮x2-2xy dx+x2y+3 dy around the boundary of the region defined by y2=8x and x=2 (a)…

Q: Rotate the region bounded by x = y² – 6y + 10 and x = 5 about the y-axis

A: Solution :-

Q: 2. Evaluate f (3x + 4y2) dA, where R is the region in the upper half-plane 15 bounded by the circles…

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Q: D Evaluate xy dady where D is Hie region bounded x=0, y=0, and x+y= ! by

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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: Evaluate E=∭D(x2+y2+z2)−3/2dV where D is the region bounded by the surfaces x2+y2+z2=9 and…

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Q: Evaluate the triple integral. SSSE2.xy dV , where E lies under the plane : = 1+x + y and above the…

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Q: Evaluate the double integral / (3x + 2) dA I D when D is the bounded region enclosed by y = x and y…

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Q: Se Si (x² + y² ) dxdy where the bounds is defined by the region shown below: y = 3 de dr y = /9 – x2…

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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: Q1 Verify that [Oy²-2x )dx +(2xy +x² xdy = [[ ƏP dA where C is the boundary of a region R R defined…

A: We have to verify ∫Cy2−2xdx+2xy+x2dy=∬R∂Q∂x−∂P∂ydA, where C is the boundary of a region R defined by…

Q: Evaluate: ∬ 〖4X d A〗 over the region R bounded by the parabola Y = X ^ 2 and the line X = Y-2.

A: Plotting the Curves on X and Y-axis : y = x2 ...............(1)y = x + 2 ..............(2)After…

Q: Evaluate the integral of the two-form w = (x8 + 2y) dx A dy over the region D bounded by the curves…

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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: 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: 1. Evaluate the double integral r²y dA, where D is the region enclosed by the x-axis and the…

A: We can evaluate the double integral.

Q: Find the integral ∭U(x2+y2)dxdydz, where the region U is bounded by the surfaces x2+y2=3z, z=3.

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Q: Evaluate the triple integral. 2xy dV, where E lies under the plane z = 1 + x + y and above the…

A: Final answer is 65/84.

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: Evaluate the triple integral. SSSE 7xy dV¸ where E lies under the plane = 1+x+ y and above the…

A: We have to Evaluate the triple integral.

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: 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: 4. Evaluate fl, cos (2) dA where D is the region bounded by D = {(x, y)/ vLT <x < V3Ln,0 <y< x² }.

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Q: 5. Evaluate , x dV where S is the region (solid) bounded by x = 0 and x =

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Q: 3. Evaluate the triple integral where E is the region behind y = 10 – 2z and in front of the region…

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Q: Find the maximum and minimum of w(x, z) = 2xz + z^2 +1 in a region R bounded by x = 0, z = 0, and x…

A: The bounded region R is:

Q: Evaluate || Vx2 +y? dx dy over the region R in the xy plane bounded by x² +y² = 36 - R

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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: 3. Let g(x,y) = Vy+1 In(x + y ) . 5 (a) Find the region D in R which is the domain of g. (b) Make a…

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

A: WE  have to solve by using green theorem  ∫F→.dr→=∫∫c∂N∂x-∂M∂ydxdy

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

A: Given that        F = &lt; √x + 6y , 3x + 6y &gt; C is the boundary of the region enclosed by y=x-x2…

Q: 4. Evaluate f, 2ry dA, where R is the region bounded by y i and

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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: Use Green's theorem to evaluate the integral: 6(-x²y)dx + xy°dy where C is the boundary of the…

A: Let C be a positively oriented, piecewise smooth, simple, closed curve and let D be the region…

Q: Q/ Evaluate (1Ox²y³-6 dA of D where D is the region bounded by : x = -2y? and x = y3.

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Q: 5. Evaluate z dV where E is the region bounded below by r2 +y² + z² = 4 and above %3D by r² + y² +…

A: We have to evaluate the integral ∭EzdV, where Eis the region bounded below by x2+y2+z2=4 and above…

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: Verify Green's theorem in the plane for S(3x² -8y )dx +(4y-6xy)dy, Where C is the boundary of the…

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Q: Evaluate the triple integral. 4xy dV, where E lies under the plane z = 1 + x + y and above the…

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Q: 5) Let D be the region bounded by the curve xy 1 and the line y = = -x. Evaluate the integral xy dA…

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Q: 2. Evaluate Jf 3ry dA, where R is the region bounded by the graphs of y = -x and y = x2, > 0 and the…

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Q: O R is the region bounded by y = 2 – x² and y = x² – 6. - %3D

A: 5.)  y=2-x2  and  y=x2-6 red line y=2-x2 blue line y=x2-6

Q: Q1 Verify that [(v ²– 2x )dx +(2xy +x³\dy = | dA where C is the boundary of a region %3D дх ду R…

A: By  apply green theorem

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 the line integral [2y'dx+(x* +6y°x)dy where C is the boundary of the R region shown below…

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