Evaluate the surface integral F• dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xz i + xj+ y k S is the hemisphere x2 + y2 + z2 = 49, y 2 0, oriented in the direction of the positive y-axis

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 F. 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…

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

A: Given- Vector field F . and the oriented surface S.          - S is the part of cone  z=x2+y2…

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 F. ds for the given vector field F and the oriented surface S. In…

A: Given- Vector field F(x,y,z)= xi^+5yj^+2zk^ and S is the cube with vertices (±1,±1,±1) To prove-…

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

A: Given vector field F(x,y,z)=x2i+y2j+z2k. The objective is to evaluate ∬SF·dS. Where S is the…

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

A: Given : The vector field F(x,y,z)=xy i +yz j +zx k  and the surface S is  z=2−x2−y2,    0≤x≤1,0≤y≤1

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

A: Given  F(x,y,z)=yi-zk We have to evaluate ∬SF.dS So by Gauss divergence theorem. ∬SF.dS=∭(∇·F)dV…

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

A: According to Gauss divergence theorem, ∬SF·dS=∭VdivFdV⋯⋯1 Here, S is the closed surface of the cube…

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 F. ds for the given vector field F and the oriented surface S. In…

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

A: We will find out the required flux.

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 F ds for the given vector field F and the oriented surface S. In other…

A: The parametric representation of the surface S is, x=x, y=2cosθ, z=2sinθ, 0≤θ≤π, 0⩽x≤5   Use the…

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 F. ds for the given vector field F and the oriented surface S. In…

A: To evaluate flux of F across S. For closed surfaces using positive orientation. Fx,y,z=x i+5y j+5z k…

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 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=-xi^-yj^+z3k^S:z=x2+y2→S:z2=x2+y2

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 F. ds for the given vector field F and the oriented surface S. In…

A: Given Fx,y,z=x i+5y j+3z k Surface S is the cube with vertices ±1, ±1, ±1 Using Gauss's divergence…

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 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: The given function is, Fx, y, z=xi^+4yj^+3zk^ The surface S is ±1, ±1, ±1 And…

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

A: Given that  F is the vector filed orientation surface s  To find the fulx of the vector

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

A: If parametric form of surface S given by r(u,v) Then flux of vector field F  along S…

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

A: It is given that for a vector field F(x,y,z)=xzeyi-xzeyj+zk and oriented surface S which is part of…

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

A: Gauss divergence theorem

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 the oriented surface 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 that     F(x,y,z) = x2i+y2j+z2k ,  We have to evaluate ∫∫sF.dS , where S is the boundary of…

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

A: To evaluate : surface integral ∬SF·dS for the given vector field F and the oriented surface S, where…

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

A: We will find out the required value.

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

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

A: To evaluate the surface integral.

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: 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…

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      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: 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:

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

A: Divergence theorem∬SF.dS = ∭V∇·F dVGiven:F(x,y,z) = -xi - yj+ z3kS is area represented by z = x2+y2…