Use Gauss' theorem to evaluate F.ndS for the given F and o. (c) F(x, y, z) = x² i+ y²j+ z² k, o : the closed surface enclosing the solid bounded by the cone z = plane z = 1. x² + y² and the

Q: Evaluate the surface integral | f(x,y,z) dS using an explicit representation of the surface. S…

A: To evaluate the surface integral using explicit  representation of the surface of function…

Q: 5. Use the Divergence Theorem to calculate the surface integral SF dS, where F(x, y, z) = (xye , xy?…

A: By divergence theorem value of the surface integral is

Q: Evaluate the surface integral. ) ر م(ل 2) ds S is the part of the cylinder x² + y2 = 16 that lies…

A:

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: Use Gauss' theorem to evaluate || F.ndS for the given F and o. (b) F(x, y, z) = x³ i+x²yj+xy k, o :…

A: (b) Fx,y,z=x3 i + x2y j+ xy k here σ is the closed surface enclosing the solid bounded by the…

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

A:

Q: Evaluate the surface integral fs F. dS where F = (4x, -2z, 2y) and S is the part of the sphere x² +…

A:

Q: Let E be the tetrahedron in space with vertices (0,0, 0), (1,0, 0), (0, 1,0), and (0,0, 1). Let F(x,…

A:

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

A:

Q: Evaluate || f (x,y,z) dS where S is the portion of the sphere centered at the origin of radius two…

A: we have the equation of sphere x2+y2+z2=22s is the portion bounded between xy plane and z=1 in the…

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

A:

Q: Use Gauss' theorem to evaluate F.ndS for the given F and o. (a) F(x, y, z) = (x – z) i+ (y – x)j+(z…

A:

Q: Evaluate the surface integral. + y2 + z2) ds S is the part of the cylinder x² + y2 = 16 that lies…

A: We will solve this problem in some steps

Q: Evaluate the surface integral. x² + y2 + z• ds S is the part of the cylinder x2 + y2 = 25 that lies…

A: Given, Where, S is the part of the cylinder x2 + y2 = 25 which lies between the planes z = 0 and z =…

Q: Miscellaneous volumes Use a triple integral to compute thevolume of the following regions.

A: The given equation of cone is and plane is, z=1-x2+y2 x+y+z=1

Q: Evaluate the surface integral. x²z² ds S is the part of the cone z² = x2 + y2 that lies between the…

A:

Q: Use Stoke's theorem to evaluate the integral xydx +x*dy– 4x'ydz where C C is the boundary of the…

A: Given: ∫Cxydx+x2dy-4x3ydzBoundry square surfaces z=1vertices are (1,0,1),(1,1,1) & (0,1,1) &…

Q: Use Stokes's theorem to evaluate OF.dr for the given F and C. (c) F(x, y, z) = xzi+ xyj– 3xz k, C :…

A:

Q: Calculate F- dS where F = (3zy', ze", z) S is the surface of the solid bounded by the cylinder y? +…

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Q: 5. Compute the Jacobian of the map G(u,v) = (u² + v²,u² – v²). %3D Find the volume of the solid…

A:

Q: Evaluate the surface integral. y² ds, S is the part of the sphere x² + y² + z² = 1 that lies above…

A:

Q: Use Stokes' Theorem to evaluate F. dr where F(x, y, z) = xi + yj +Xx² + y² )k and C is the boundary…

A: Stokes theorem: ∮f→·dr→=∬S curl f→·n^ ds Given F(x, y, z)=xi + yj+9(x2+y2)k and C is the boundary of…

Q: Calculate F.dS where F = (3ry", re", z*) S is the surface of the solid bounded by the cylinder y + z…

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Q: (b) Verify Stokes' theorem on a region which is a portion of the sphere r2 +y² +2 16 which lies…

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Q: Evaluate the surface integral, f(x.y.z) dS using an explicit representation of the surface. f(x.y.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 planes…

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

Q: Evaluate the surface integral: || G(x, y, z) ds for G(x,y,z) = z², where S is the portion of the…

A:

Q: Evaluate the surface integral. (z + x2y) ds S is the part of the cylinder y2 + z2 = 16 that lies…

A: Given ∫∫S(z+x2y)dS where S is the part of the cylinder y2+z2=16 that lies between the planes x=0 and…

Q: a) Integrate g(x,y,z) = Inx²+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

A:

Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

A: Given ,                                                                             F(x,y) =…

Q: Let S denote the part of the cone z = Vx2 + y? that lies between the surfaces z = 2 + sin(xy) and z…

A: Given : S denotes the part of the cone z=x2+y2 that liesbetween the surfaces z=2+sinxy and…

Q: Evaluate the surface integral. x2z2 dS S is the part of the cone z2 = x2 + y2 that lies between the…

A: Given: The surface integral is given as, S is the part of the cone z2-x2 + y2 that lies between the…

Q: 10. Let S be the surface of the solid bounded by the paraboloid z= the plane z=4 as in the picture.…

A: Given: x² + y² = z and z = 4

Q: Use Gauss’ theorem to evaluate F.ndS for the given F and o. (b) F(x, y, z) = x³ i+x?yj+xy k, o : the…

A: We will use gauss divergence theorem to find value of given surface integral  If E is a  simple…

Q: Evaluate G if G is a solid in the first octant bounded by the plane y +z = 2 and the surface y = 1–…

A: Use the following formulae, to obtain the solution. a-b2=a2-2ab+b2∫xndx=xn+1n+1+C

Q: E is the solid in R3 bounded by the cone surface z = square root (x2+ y2 ) and the plane z = 3, and…

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Q: Evaluate f. F dS where F(x,y, z) = (4x³z, 4y³z, 3z*) and S is the surface of the solid bounded by…

A:

Q: (b) Evaluate the surface integral ƒ (x, y, z)dS where f(x,y, z) = z² and S is a portion of the cone…

A:

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: Let S be the piece of the surface z = 9– x2 that lies inside the cylinder x2 +y? = 9, and let F =…

A: According to question, Given Surface, z = 9 -x2 ,This surface lies Inside the cylinder x2 + y2 = 9,F…

Q: Use the Divergence Theorem to evaluate ∬SF⋅dS∬SF⋅dS , where…

A:

Q: Use Gauss' theorem to evaluate F.ndS for the given F and o. (b) F(x, y,z) = x³i+x²yj+xyk, o : the…

A: Gauss theorem states that ∫∫σ F.ndS=∬∫V div(F) dVwhere V is the volume inclosed by the closed…

Q: Calculate F. dS where F = (3xy°, xe", zª) S is the surface of the solid bounded by the cylinder y? +…

A: Let's find.

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: 1. Evaluate the surface integral [[' xz² ds ; o is the part of the cone z = x² + y² that lies…

A:

Q: Use Stoke's theorem to evaluate the integral xydx+x'dy – 4x’ydz where C is the boundary of the…

A: Here the surface is the plane of the square with vertices A1,0,1, B1,1,1, C0,1,1 and D0,0,1.  To…

Q: 1. Evaluate the surface integral SL xz² ds ; o is the part of the cone z = Vx2 + y² that lies…

A:

Q: Evaluate the surface integral. v² as S is the part of the sphere x2 + y2 + z2 = 64 that lies inside…

A: A scalar function f(x,y,z) is a rule that is used to associate a number or quantity with a…

Q: Integrate G(x, y, z) = x + y + z over the surface of the cube cut from the first octant by the…

A: Definition used: