If E is the solid shape bounded by x 2 0,y 20 ,z 2 0 and the plane 2x + 3y +z = 6 evaluate (x + y) dV

Q: 1. A solid G is bounded by the paraboloid z = 4 – x² – y², the cylinder x² + y? = 4 and the plane z…

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Q: Triple integrals Use a change of variables to evaluate the following integral.

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Q: Find fff y av, y dV, where E is the solid bounded by the parabolic cylinder z = ² and the planes y =…

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Q: Let S be the solid bounded by the planes z = o and y + z = 3, and the cylinder x2+y2 =2y-

A: answer is in next step

Q: If F= 2y I- 3J +x²k and s the surface parabolic cylinder y= 8x in bounded by the planes OF the 2.…

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Q: Consider the PDE y Ur + a Uyy + Uz – Uy = r² + y? In what region of the xy-plane is this PDE…

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Q: . Evaluate (x² + y) dv G if G is the solid bounded by the parabolic cylinder z = y², xy-plane and…

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Q: Calculate F - dS where F (e* sin y, e² cos y, yz²) S is the surface of the box bounded by the planes…

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 6x + 12y + 18z on the elipse…

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Q: Let R denote the solid in the first octant bounded by the planes 2x + 6y + 3z = 6, x = 0, y = 0, z =…

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Q: Calculate F. dS where S F = (e" sin y, e* cos y, yz²) and S is the surface of the box bounded by the…

A: Given Data: Integral: ∬SF→·dS Vector: F→=exsiny, excosy, yz2 Planes: x=2, y=4, z=3 The divergence of…

Q: The solid bounded by x = y? – 1, z = 1 – y², z = 4 – x, and z = 0.

A: Given that,

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 6x + 12y+ 18z on the elipse…

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Q: Evaluate /// 203 dV G if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: Here we have to find range of values for x,y and z and then find triple integral

Q: a) Let G be the wedge in the first octant that is cut from the cylindrical solid y² + z² ≤ 4 by the…

A: To Evaluate: ∫∫∫GxyzdV. Where G: y2+z2≤4, y=2x , x=0. As per policy, we are solving only thr first…

Q: Calculate S," (2x+y) dV where V is a closed space bounded by the cylinder z = 4 – x2 and the planes…

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Q: Calculate ff F.n dS where F x'yzi + 2xj + y?k in the solid region S bounded by the parabolic tube z…

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Q: A solid G is bounded by the paraboloid z = 4 – x2 – y², the cylinder 22 + y? = 4 and the plane z =…

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Q: If S is the solid bounded by the paraboloid z = 3x2 + 3y and the plane z = 4 (with constant…

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Q: Let f(x, y) = 2x and C be the line segment on the plane from (0, 0) to (3, 4). Evaluate the line…

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Q: Calculate . (VxF). n dS if F = (x + 2y)i – 3zj + xk and S is a 2x+y+2z=6 plane surface bounded by x…

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Q: • SSS ²³² x² + y² = 2, and the xy plane. Evaluate e² dV where E is enclosed by the paraboloid z = 6…

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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: Evaluate ∫∫∫E √x2 + z2dV, where E is the region bounded by the paraboloid y = x2 + z2 and the plane…

A: Given, y=x2+z2 ⇒z2=y-x2z=±y-x2 Therefore the limit of z is -y-x2≤z≤y-x2 On drawing the graph in the…

Q: 2. A solid G is bounded by the paraboloid z = 4-²-y², the cylinder x² + y² = 4 and the plane z = 5.…

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Q: If E is the solid shape bounded by x 20,y 20,z 20 and the plane 6x + 4y + 3z = 12 evaluate %3D (y +…

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Q: 2. Evaluate ([.(Vx F). ds, where S is the surface of the paraboloid x2 + y2 + z = 4 above the…

A: We have given F→=(x2+y-4)i+3xyj+(2xz+z2)ksurface is given x2+y2+z=4 and above the xy planediagram of…

Q: Evaluate the triple integral (* + 1y) dV where E is bounded by the parabolic cylinder y = 32² and…

A: We have to find the triple integral  ∫∫∫E(x+y)dVwhere E is bounded by the parabolic cylinder y=3x2…

Q: Consider the PDE y u + Uyy + u, - Uy = 2 +y? In what region of the xy-plane is this PDE elliptic? xy…

A: The objective is to find in what region of the xy-plane the pde is elliptic.

Q: 3. Evaluate /// 2* dV if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: triple integral

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: Calculate ( (2x + y) dV , where V is a closed space bounded by the cylinder z = 4 – x? and the…

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Q: É = ( 2x3 + y°, y3 + z³, 3y²z), S is the surface of the solid bounded by the paraboloid z = 1– x2 –…

A: We will find out the required flux.

Q: 4. Evaluate //F FdS, where F(x, y, z) = (2x + 2xz, -4xy², y - z2) and R R surface of the solid…

A: The given problem is to evaluate the given surface integral over the given solid surface bounded by…

Q: A solid G is bounded by the paraboloid z = 4 – x2 – y?, the cylinder x2 + y? = 4 and the plane z =…

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Q: Find y dV, where E is the solid bounded by the parabolic cylinder z = = 2 and the planes y = 0 E and…

A: The solution is given below

Q: (a) Given F(x, y, z) = –xi– y j+x²k and o is the surface of the solid bounded by the Vx² + y² and…

A: There is no specific introduction for this question. Please go through the solution.

Q: please help me as soon as possbile

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Q: Find II| y dV, where E is the solid bounded by the parabolic cylinder z = x² and the planes y = 0 E…

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Q: Evaluate (x + 5y) dV where E is bounded by the parabolic cylinder y = x² and the planes z = 3x, y =…

A: given is  a partial differential equation in dX , dY, dZ we can partially integrate the given…

Q: Let S denote the part of the cylinder x2 + y² = 9 that lies between the planes r + y = 1 and x – y =…

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Q: c, y, z) = x²zi + xz'j+ y ln(x + 1) k, s the surface of the solid bounded by the 2z = 4, y = 3, x =…

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Q: Evaluate the triple integral -p (x + 6y) dV where E is bounded by the parabolic cylinder y = 8x² and…

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Q: Evaluate (x² + y) dv G if G is the solid bounded by the parabolic cylinder z = the planes x = 0, x =…

A: Here I am using simple tripple integration to solve this question.

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: 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: Use Stokes’ Theorem to evaluate F(x, y, z) = 3zi + 4x j + 2yk; C is the boundary of the paraboloid…

A: Use Stokes theorem

Q: 3xy dV, where E is bounded by the parabolic cylinders y = x² and x = y and the planes z = 0 and z =…

A: It is given that, y=x2 and x=y2 and the planes z=0 and z=7x+y. Define the region E as follows.…

Q: 36. Ifo = 45x y, evaluate ||] q o dV where V is the closed region bounded by the plane 4x +2y +z =…

A: The solution is given as