O R is the region bounded by x² + y – 4 = 0 and x – y +2 = 0 an is revolved about y = 0.

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: x² sin xy 14.5.8. || - dA(x, y), if D is the region bounded by æ² = "4, x² = TY, y² = ;, and D y? =…

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

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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: 8. Evaluate y° dx – x° dy, where C is the boundary of the region R = {(x,y) E R² : x² + y² 0}…

A: Applying conditions

Q: Let R be the region bounded by y = 4x + 2, y = 4x + 5, y = 3 - 2x and y = 1-2x. Which one of the…

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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: ex: Evaluate SS (&++y²)dV over the first octont region boundeol by the cylinders x*ty=/ and xay=4…

A: Convert coordinate system into cylinder coordinate system. Sketch region D and find range of…

Q: Evaluate (2r+y) dV _ where V is closed region bounded by the z= 4>x and the planes x = 0, y = 0 and…

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Q: Evaluate fSR f(x, y) dx dy, where R is the region given by 0<x < 2;0 < y < 5 and f(x, y) = 1 – ² –…

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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: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the cone z = Vr2 + y²…

A: In cylindrical coordinates,                                                               and…

Q: and above the region D in the ry-plane given by D = {(x, y) E R² | 0 < y < 1, y < z< Vy}.

A: Given  Surface : z=e5xx-x5 Region D=x,y∈R2| 0 &lt;y &lt; 1, y &lt;x &lt;y5

Q: (b) |(x+y)dA} where R is the region bounded by y=Jx and y = x² .

A:

Q: 3. Use Green's Theorem to evaluate (e3x +y²)dx + (sin y – x²)dy where C is the boundary of the…

A: Green's theorem

Q: Let f(x,y)=(x+y)² and D the region defined by D=((x,y); x² +y²sa?) then the double integral…

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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: 5. Show that, in the region bounded by y = Vx and y = x2 the following double integral 3 (х + у) dA…

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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: Evaluate f S Sp(2+ e(=²+v²+z*)*/²) dV, where B = {(x, y, z) | x² + y² + z² < 9} Describe the region…

A: Consider the provided question, (2) (a)

Q: ]]] xyz dV if S is the region bounded above by x² + y² +2²= 16 and below the S cone 2 = √² + y² with…

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Q: - The region bounded by 2y = x and (x − 2)² = −4y + 12 is revolved about the line y = 4. Determine…

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Q: Use Green's Theorem to evaluate |(e* +y²) dr + (+r²) dy where C is the boundary of the region…

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Q: Evaluate the double integral S, x dx dy where the region R is bounded by: 9 y = 4x – 3, 1 +x. 4 у %3…

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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: 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: (2) Consider the region D in the ry-plane which is bounded by the following 2 4 curves y =, y = ỷ =…

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Q: 12 O f. T 4 .4 4-y If R is the region such that || e dA = TI e" dr dy, then the area of the region R…

A: Area of region =double integration dx *dy

Q: ) Evaluate Sxy dx dy R is the region bounded by x =0, x =2, y = x

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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: 2. Evaluate [(3yz)dV where B is the region in the first octant lying below the plane x + 2y +2: = 4.

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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: SSR (r + y)2 dA, where R is the region bounded by the limaçon r = 2 + cos 0

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Q: x² and t %3D 2) = z where E is the region bounded by the parabolic cylinder y

A: We have to set up the integral according to the given information

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: Use Green's Theorem to evaluate (eš + y³)dx + (sin y – x²)dy where C is the boundary of the region…

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Q: Verify that | (y -2x)dx + (2.xy + x² = [] dA where C is the boundary of a region R ây C R defined by…

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Q: The region D bounded by y = 0 and y = -1+a² is shown in the following figure. Is this region of Type…

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Q: (e) | x+y dA where R is the region bounded by y=0, y=x², R and x=1/3.

A: Let's find.

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: xyz dV where E is the region bounded by = y², x² = y, z = xy y z = 0.

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Q: 2. Evaluate Vye"V dA where D is the region bounded by y = x² and y = 4.

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Q: Evaluate z dV where E is the region bounded between the spheres x² + y² + z² = 1 and x² + y? + z° 4…

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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: 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: where E is the region bounded by the paraboloid y= r+ z2 (Figure 15.4. %3D y = x2 + z?

A: Please rate and feel free to ask any query about any part of the question .

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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