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…

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

Q: Evaluate the line integral fe F n ds, where the vector field F(x, y) = (tan-'(y) + x², x?y) and C is…

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Q: Consider the force field F(x, y, 2) i+ x² cos z + j+ -k (a) Use Gauss' theorem to find the flux…

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

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

A: Given  Fx,y,z=xi+yj+z4k S is the part of the cone beneath the plane z=1 with downward direction. Use…

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

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Q: use the surface integral in Stokes’ Theorem to calculate the circulation of the field F around 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: 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: We have F(x,y,z)=yj-zk, S consists of paraboloid y=x2+z2, 0≤y≤1, and the disk x2+z2≤1, y=1. We have…

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

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Q: Having trouble with this problem and there is no 'practice another problem' to help me figure it…

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Q: Let Tbe the solid region in the first octant bounded by the surface S = S1 + S2, where Si is the…

A: Consider the given information: T be the solid region in the first octant bounded by the surface…

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: 12. Evaluate the surface integral JJ, F ·dS for the vector field F(x,y,z)=(-x,-y,z'), where S is the…

A: This is the problem of multivariable calculus, surface iuntegral.

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: Let o be sphere of radius a, centered at the origin, oriented by the outward unit normal n. Let F =…

A: Let σ be sphere of radius a , centered at the origin oriented by the outward unit normal n .Let  F→…

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: 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: Find the surface integral of the field F(x,y,z)=9xi +9yj +9zk across the portion of the sphere x² +…

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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 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…

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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: 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: From the given statement, the vector field

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: 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 triple integration uses the volume element for integration. The volume element for triple…

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

A: To evaluate the surface integral.

Q: Let F = x?i+y?j+z²k, S be part of the surface 22 = supplied with the unit normal field i for which i…

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Q: Let S be the surface in R' that is the part of the ellipsoid 2x2 + y² + z? = 2 satisfying y > 1.…

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

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Q: Let E be the union of the two surfaces , and E2 given by E1 : y? + 22 = 4, 1 2, oriented with…

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

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

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Q: Given the radial field (x, y, z) r (x2 + y? + z2)3/2 r|3/2 Find the outward flux across the sphere…

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Q: 1 Find the line integral | Fdrof the vector field F :(xi + yj+ zk) where C is the boundary of the…

A: see below the answer

Q: Evaluate the line integral J F. · dr for the vector field F = cos(x)i+ sin(y)j+ x²yk along the curve…

A: Given:  F=cosxi+sinyj+x2yk, rt=t2i+t2j+tk, 1≤t≤3 So, drdt=2ti+2tj+k We know that rt=xti+ytj+ztk So,…

Q: 2. Let S denote the piece of parabolic surface x2 + y? = z, 0 < z < 4. For the vector field F(x, y,…

A: According to the given information, Let S denote the piece of parabolic surface as:

Q: find the surface integral of the field F over the portion of the given surface in the specified…

A: