„ Compute the flux of F = xi + yj + zk through the curved surface of the cylinder x? + y² = 1 bounded below by the plane x + y + z = 1, above by the plane x + y+ z = 5, and oriented away from the z-axis. flux = 12*pi

Q: 6. Find the flux of F (x,y, z) = y cos(z) i – y x sin(x)j+xy³k through the outward oriented cube of…

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Q: Let S be the portion of the cylinder y = ln x in the first octant whose projection parallel to the…

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Q: Compute the flux of F = 3(x + z)i +j+ 3zk through the surface S given by y = x2 + z2, with 0 0, z 2…

A: flux is determined as shown below

Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

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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…

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Q: (a) Evaluate ([ Á.ds where A=(x+y²)î-2xj+2yzk and s is the surface of the plane in the first octant…

A: For the detailed solution of the problem follow the next steps.

Q: Let S be the cylinder x +y = a°, 0szsh, together with its top, x² +y° sa, z=h. Let F= - 4yi + 4xj +…

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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: Compute the flux of F = 3(x + z)i +j+3zk through the surface S given by y = x2 + z2, with 0 0, z >…

A: From given data we see that the surface is oriented towards xz plane,  Hence,  d→s=dxdzj→

Q: Use the Divergent Theorem to find the outward flux ofF = yi+3yj+ 322k across to the boundary of the…

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Q: Use Divergence Theorem to evaluate SF. Nds and find the outward flux of F(x,y,z) = xi+y²j−zk through…

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Q: Use the Divergence Theorem to find the flux of F(x, y, z) = (x – z)i + (y – x)j+ (z – y)k %3D -…

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Q: 2). Find the flux of F(x, y, z) = (0, yz, z) outward through the surface S cut from the cylinder y +…

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Q: Find |[F•N dS (flux), where F(x, y,z)= 4x'zi +4y'zj+3z*k, S is the sphere with radius R centered at…

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Q: Find the outward flux of F through S. F-Ñ dS where F(z, y, z) = -3zî+y³j+yk, and S is the surface of…

A: The general form of a vector valued function in three dimensions is given by F→=F1i^+F2j^+F3k^,…

Q: d) An open surface F is given by F = {(x,y, z) |z = 4 – x² – y² , z > 0} . Compute the flux of V…

A: V(x,y,z) = <2x+3y,2y+3x,-4z>F={ (x,y,z) : z=4-x2-y2 , z≥0}Consider, g(x,y,z) = z+x2+y2-4…

Q: Compute the flux of F = (5(z + 2), 5, 52) through the surface S given by y = ² + 2, with 0 0, z 2 0,…

A: We have to find flux.

Q: 4. Find the flux of F = across the curved sides of the surface S = {(r, y, z)|z = cos y, |y| < T,0 <…

A: we have F→=e-y,2z,xy Surface S=x,y,zz=cosy,y≤π,0≤x≤4 Let z=gx,y=cosy ∂g∂x=0,∂g∂y=-sinyy≤π…

Q: 3. Calculate the rotational flow of F(x, y, z) = -j + xj + x²k, that goes through the cone given by…

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Q: Compute the flux of F= xi+yj+ z*k across the cone z =Vx2 + y? , 0szs1, in the downward direction.…

A: We have to find the flux in the downward direction.   Let us assume that x=rcosθ, y=rsinθ, z=r Then…

Q: Use a parameterization to find the flux do of F = z²i+ xj – 4zk in the outward direction (normal…

A: Apply Divergence theorem to the given surface integral, ∬F.ndσ=∫∫∫DivFdV

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…

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Q: Compute the net outward flux across the sphere r²+y²+z (r*, y², 2ª).

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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: 7. Find the flux of F(x, y, z) = x î+ y ĵ+ z² k across the sphere of radius 1 centered at the origin…

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Q: 5. Find the flux of F (x,y,z) = y cos(z)i-yx sin(x) j+ xy³k through the outward oriented cube of…

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Q: Find the flux of F= through of the total surface of the closed cone y=(x2+z2)0.5 with 0 < y < 2…

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Q: Integrate F =-(y sin z)i + (x sin z)j + (xy cos z)k around the circle cut from the sphere x2 + y2 +…

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Q: Find the outward flux of F = across the boundary of D: the upper region cut from the solid sphere…

A: To find the outward flux use divergence theorem

Q: 8. Use the divergence theorem to evaluate the flux integral OF-nds where F(x,y.z)= (x' +…

A: Given: F (x, y, z)= x3+cotan-1(y2z3), y3-ex2+z3, z3+ln(x-y)  n is the outward unit normal to S, and…

Q: Find the flux of F = yi+2xj-3zk through the unit disk centered at (0,3,0) in the plane y=3, oriented…

A: Given F→=yi^+2xj^-3zk^ through the unit disk centered at 0,3,0 in the plane y=3 oriented towards the…

Q: Use the Divergence Theorem to find the flux of F(x, y, z) = 3x³i + 3x²yj + 24xyk across the surface…

A: Flux of a vector field over a closed surface is equal to the divergence of the field in the volume…

Q: Find the flux integral ∫∫scurl(F).dS, where F(x,y,z) = [-y + 2cos(πy)e2x + z2, x2cos(zπ/2) -…

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Q: use divergence theorem to find the outward flux of f =2xzi-3xyj-z^2k across the boundary of the…

A: By divergence theorem

Q: Using Green's Theorem, find the outward flux of F across the closed curve C. F = (-5x + 2y) i + (6x…

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Q: 7. Find the flux of F(z,y, 2) = ri+yj+zk through the portion of the paraboloid z = 1+z²+y° that is…

A: Given

Q: 6. Compute the flux of F = [0, 0, z²] through the spherical surface S given as the upper hemisphere…

A: To find- Compute the flux of F→ = 0, 0, z2 through the spherical surface S given as the upper…

Q: Find the flux of F(x, y, 2) = (r, y, 2) across the surface o which is the surface of the solid…

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Q: 5. Compute the flux of F(r, y.2) =zi- 2yj+ 2ak across the surface of the cylinder bounded by a+y =9…

A: Solve the problem as shown below.

Q: 4. Consider a soup can of height 2 and radius 3, whose base (bottom) lies in the r- y plane and is…

A: Given- Consider a soup can of height 2 and radius 3, whose base (bottom) lies in the x-y plane and…

Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

A: Given surface, F=2xyi+2yzj2xzk           ...(1) Given plane, x+y+z=2a                ...(2) Where…

Q: Let S be the cylinder x² + y² =a²2, 0≤zsh, together with its top, x² + y² sa², z = h. Let F = -7yi +…

A: Given : Surface S is the cylinder x2+y2=a2, 0≤z≤h, together with its top, x2+y2≤a2, z=h and  F→=-7y…

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) = Inx²+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

A:

Q: Use the Divergence Theorem to evaluate N ds and find the outward flux of F through the surface of…

A: We have to find the flux

Q: Calculate the flux of F across G. F(x, y, z) = 2xi + 2yj + 2zk; G is the surface of the sphere x2 +…

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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…

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