Evaluate the surface integral || F·dS for the vector field F(x, y,z)=3yi– 3xj+6zk where S S consists of the hemisphere x +y² +z° = 4 , z> 0 and the disk x² + y° <4, z = 0 with negative orientation. %3D

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A: Given F(x,y,z)=x2i+y2j+z2k and S is the boundary of the solid half-cylinder .

Q: Evaluate the surface integral F · dS for the given vector field F and the oriented surface S. In…

A: Given vector field is Fx,y,z=xi^-zj^+yk^. To find the flux of F across the surface S , the part of…

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Q: Evaluate the surface integral∬SF ⋅ dS for the given vector field F and the oriented surface S. In…

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Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A: To find the surface integral ∬F.ds by using gauss's divergence theorem∫∫sF.ds=∫∫∫vdivF dv  where v…

Q: Evaluate the surface integral / F. ds for the given vector field F and the oriented surface S. In…

A: Solution:- We know that ∫∫sF→·dS→=∫∫D-P∂g∂x-Q∂g∂y+RdA······(1) where P,Q and R are component…

Q: Consider the vector field F(x, y, z) = (x, Y, 9z). Evaluate the surface integral I = ls F. dS where…

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Q: Evaluate the surface integral ∫∫s F. dS for the given vector field F and the oriented surface S. In…

A: Given that: Fx,y,z=x2i+y2j+z2k, S is the boundary of the solid half-cylinder 0≤z≤√1-y2 ,0≤x≤2 Let S…

Q: Let S be the surface z = 1 – x² – y², z > 0, supplied with the field of unit normals n such that n ·…

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Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A: Use the divergence theorem to evaluate the surface integral. div F=∂F∂x+∂F∂y+∂F∂z=2x+y+z Therefore,…

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

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Q: i F - y,-1 is vector field and R = {(r, v): 45 2 + y s 9, y S -z} is region in zy- plane. R is the…

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Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A:

Q: Evaluate the surface integral F. dS for the given vector field F and the oriented surface S. In…

A:

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A:

Q: Evaluate the surface integral F. dS for the given vector field F and the oriented surface S. In…

A:

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A: Given  Fx,y,z=x2i+y2j+z2kand 0≤z≤9-y2 , 0≤x≤2

Q: Evaluate the surface integral || F. dS for the given vector field F and the oriented surface S. In…

A: Consider the provided question,

Q: Evaluate the surface integral F. dS for the given vector field F and the oriented surface S. In…

A: According to question given that F(x,y,z)=xy i + yz j + zx kz=6-x2-y2 that lies above the square…

Q: Verify Stokes' theorem for the vector field F(x, y, z) = zî + xj+ yk taken over the half of the…

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Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A:

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A:

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

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: Evaluate the surface integral F. dS for the given vector field F and the oriented surface S. In…

A: Gauss divergence theorem

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Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A:

Q: aluate the surface integral F. dS for the given vector field F and the oriented surface S. In other…

A: Given,        F→(x, y, z)=yi^-xj^+5zk^   and    x2+y2+z2=4, z≥0

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A: The given problem is to evaluate the given surface integral in the part of the cone  between the…

Q: Evaluate the surface integral      SF · dS  for the given vector field F and the oriented surface…

A: To evaluate the surface integral.

Q: Verify Stokes' theorem for the vector field F(x, y, z) = zî + xj+ yk taken over the half of the…

A: According to the given information it is required to verify the stokes theorem for the given vector…

Q: Evaluate the surface integral F. dS for the given vector field F and the oriented surface S. In…

A: Given the surface is the part of the cone z=x2+y2 between the planes z=-1 and z=3 with the downward…

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A:

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A: Given function is, Fx,y,z=-xi^-yj^+z3k^ z=x2+y2 Between the pairs z=1 and z=4. then the flux of…

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A: In this question, we use the div.  theorem to evaluate the surface integral. given that…

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Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

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

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A:

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A: Consider the vector field F(x,y,z)=xi-zj+yk =Pi+Qj+Rk Use spherical coordinates…

Q: Evaluate the surface integral / F. ds for the given vector field F and the oriented surface S. In…

A: Given  Fx,y,z=-xi-yj+z3k and S is the part of the cone z=x2+y2 between the planes z=1 and z=6 with…

Q: Evaluate the surface integral F. dS for the given vector field F and the oriented surface S. In…

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Q: Evaluate the surface integral      SF · dS  for the given vector field F and the oriented surface…

A:

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A:

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A: Given surface is beneath the cone z=x2+y2 and between the planes z=1 and z=3. Hence in cylindrical…

Q: Evaluate the surface integral F. dS for the given vector field F and the oriented surface S. In…

A: Step:-1 Note:-  Flux = ∬S F.dS Given that Fx, y, z =xy i +yz j +zx k and S is the part of paraboloid…

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A: Given that F(x,y,z)=yi-xj+5zk and S is x2+y2+z2=4 The objective is to find the ∬F.dS Take…