Calculate ( (2x + y) dV , where V is a closed space bounded by the cylinder z = 4 – x? and the planes x = 0, y = 0, z = 0 dan y = 2.

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

A: Here, F=<exsiny,excosy,yz2>

Q: Calculate F· dS where F = (3xy', ze", 2°) and S is the surface of the solid bounded by the cylinder…

A: We need to calculate ∬SF→.dS which is the flux. Now, we can use the divergence theorem to find…

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: Verify Green's theorem in a plane with respect to S. [(x2 - y²)dx + 2xy dy], where C is the boundary…

A: Using greens theorem

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: Integrate G(x, y, z)=x4 y ( y2 + z2 ) over the surface of the cylinder y2 +z2 = 25 that lies in the…

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Q: 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)…

A: The given question is solved below

Q: 4. Find the volume V of the solid S that is bounded by the elliptic paraboloid defined by 2x2 + y2…

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

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Q: Let S be the portion of the cylinder y² + z² = 4 with z > 0 between the planes r = 0 and a = 5…

A: To compute the flux of below function F across S F=x2,y2,z2

Q: Integrate G(x, y, z) = y + z over the surface of the wedge in the first octant bounded by the…

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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 F - dS where F = (e² sin y, e² cos y, yz²) S is the surface of the box bounded by the…

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Q: Let I = , zdV ,where D is bounded by the planes x = 0, z = 0, x+ y = 2 and the cylinder x2 + z2 = 1…

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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: Use the Divergence Theorem to evaluate (5x + 10y + z) ds where S is the sphere x2 + y2 + z2 = 1.

A: In the given problem, S is the sphere x2+y2+z2=1Divergence Theorem:∬SF·n dS=∭Ediv F dVNow, the…

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

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Q: Use divergence theorem to evaluate where F(x, y, z) = 3xyi + xyj + 2zk and s is the surface of the…

A: Given ; F(x,y,z) = 3xyi + xyj + 2zk

Q: Integrate R(x,y,z)=x (xy2 +z) over the surface of the cylinder x2 + y2 = 9 that lies between the…

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

A: Given : F=ex sin y,ex cos y,yz2x=1;y=2 ;z =5step 1:By using divergence…

Q: Evaluate. where G is a solid that lies in the first octant bounded by x^2 + y^2 = 3z and z = 3.

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

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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: Integrate G(x, y, z) = x - y - z over the portion of the plane x + y = 1 in the first octant between…

A: Given G(x,y,z)=x-y-z

Q: Evaluate || F-n dS where S is the cylinder (including the disk on the bottom) x² + y² =1 for 0<z<1…

A: First, we plot the given surfaces.Cylinder : x2+y2=1; 0≤z≤1Paraboloid : 3x2+3y2+z = 4; 1≤z≤4.

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

A: Given F¯={exsiny,excosy,yz2)

Q: Evaluate the triple integral. SSS 5x²e" dv I where E is bounded by the parabolic cylinder z = 1 - y²…

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

A: We have to find double integral of F. ds

Q: Let D be the solid region bounded above by z = -5x² +y? and below by z =-5. Then the projection of D…

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Q: Integrate g(x, y, z) = x4y(y2 + z2 ) over the portion of the cylinder y2 + z2 = 25 that lies in the…

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Q: Use the Divergence Theorem to evaluate (3x + 2y + z2) ds where S is the sphere x2 + y2 + z² = 1.

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Q: Calculate F- dS where F = (3ry², re², z³) S is the surface of the solid bounded by the cylinder y? +…

A: The general form of a vector-valued function in three dimensions is given by F¯=F1,F2,F3, where F1,…

Q: Find the centroid of the solid bounded by the parabolic cylinder 1- y? and the three planes given…

A: To find the centroid of the solid bounded by the parabolic cylinder: The region is defined as…

Q: please help me as soon as possbile

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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: A: Determine the mass and center of mass of the solid that bounded by the paraboloid z = 9y? + 9x?…

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

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Q: Use the Divergence Theorem to evaluate (4x + 3y + z) dS where S is the sphere x2 + y2 + z2 = 1.

A: The divergence theorem establishes the equality between surface integral and volume integral.

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

A: We need to find the surface integral. We will need basic knowledge of parametrization of vector…

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 the triple integral zdV, where E is bounded by the cylinder y² + 2² = 4 and the planes z =…

A: Given problem:- Evaluate the ∫∫∫E z dV, where E is bounded by the cylinder y2+z2=4 and the planes z…

Q: . Integrate f(x, y) = cos (x² + y²) (a) over the closed unit disk; (b) over the annular region 1 <…

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

Q: Find the flux of F across S, where F(x, y, z) = xyi + y²j + zk and S is the part of the paraboloid z…

A: According to question given that F(x,yz,)=xyi^ + y2 j ^+z k^S is the part of the paraboloid z=x2+y2,…

Q: (a) Integrate g(x,y,z) = lnx'+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: 2. The solid in the first octant bounded by the planes x = 0, y = 0, z = 1, z = 2 – y, and the…

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