Calculate F- dS where F = (3ry², re², z³) S is the surface of the solid bounded by the cylinder y? + z² = 1 and the planes a = 3 and z = - 1

Q: Calculate F dS where S F= (4x°z, 4y°z, 3z*) S is the surface of the solid bounded by the hemispheres…

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Q: Find the area of the surface x2 + y2 - z = 0 that is cut from above by the plane z = 4

A: Surface is given by x2+y2=z Area=∫∫R2x2+2y2+1dA       =∫∫R4x2+4y2+1dA Let x=rcosθ and y=rsinθ…

Q: Use Stokes' theorem to evaluate (V x F) - dS where F(x, y, z) = -6yzi + 6rzj + 5(x2 + y²)zk and S is…

A: Given that F(x,y,z)=-6yzi^ + 6xz j^+ 5(x2+y2)z k^ Calculating the curl,…

Q: Calculate F· dS where F = (3xy', ze", 2°) and S is the surface of the solid bounded by the cylinder…

A: We need to calculate ∬SF→.dS which is the flux. Now, we can use the divergence theorem to find…

Q: Calculate | F. dS where F = (4z°z, 4y°z, 3z*) S is the surface of the solid bounded by the…

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Q: Calculate F· dS where F = (4x*z, 4y°z, 3:*) S is the surface of the solid bounded by the hemispheres…

A: Given

Q: Calculate F - dS where F (e* sin y, e² cos y, yz²) S is the surface of the box bounded by the planes…

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Q: Evaluate JS yz + 4ryds where S is the surface of the solid bounded by 4x+2y+z=84, z=0, y=0 and x=0.…

A: Use the divergence theorem to find the surface integral,…

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

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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: Find the sum of maximum and minimum values of the function f(x, y, z) = 9x + 18y + 27z on the elipse…

A: Using Lagrange Multipliers with Two Constraints to find the maximum and minimum values of the given…

Q: Find the area of the surface of the paraboloid f(x, y) = 2 − x2 − y2 Paraboloid that lies above the…

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Q: Evaluate the surface integral. z + x2y x²y) ds S is the part of the cylinder y² + z2 = 9 that lies…

A: We have to find the surface integral from the given condition

Q: Evaluate the surface integral. /| x*yz ds, s is the part of the plane z=1+ 2x + 3y that lies above…

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Q: Find the flux of F (x, y, z) = 4.xi+ 4yj+ 2k outward (away from the z-axis) through the surface cut…

A: The field lines of a vector field F through surfaces with unit normal n, the angle from n to F is θ.…

Q: Calculate F . dS where F = (4x°z, 4y°z, 3z*) S is the surface of the solid bounded by the…

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Q: Find the sum of maximum and minimum values of the function f(x,y, z) = 8x + 16y + 24z on the elipse…

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Q: Evaluate the surface integral.∫∫S (x2+y2+z2) dS, S is the part of the cylinder x2+y2 = 9 between the…

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

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Q: Calculate F . dS where F = (4x°z, 4y°z, 3z*) S is the surface of the solid bounded by the…

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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: A solid G is bounded by the paraboloid z = 4 – x2 – y², the cylinder 22 + y? = 4 and the plane z =…

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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: Calculate F. dS where F = (e" sin y, e² cos y, yz²) S is the surface of the box bounded by the…

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Q: Evaluate the surface integral. J[x²³x² x²yz ds, S is the part of the plane z = 1 + 2x + 3y that lies…

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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: Integrate R(x,y,z)=x (xy2 +z) over the surface of the cylinder x2 + y2 = 9 that lies between the…

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Q: Calculate F. dS where F = (4x°z, 4y*z, 32*) S is the surface of the solid bounded by the hemispheres…

A: Given that F→=(4x3z, 4y3z,3z4) and S is bounded by z=16-x2-y2, z=1-x2-y2, z=0 Now,…

Q: Calculate F. dS where F = (e* sin y, e² cos y, yz²) S is the surface of the box bounded by the…

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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: Use divergence theorem to evaluate F·dš where F(x,y, z) = (2x + yz)ī + 2yzj – z?k and S is the…

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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…

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Q: Evaluate F. dS where: F(x, Y, z) = yi+xj+ zk, S is the boundary of the solid region E enclosed by…

A: Given F⇀x,y,z=yi^+xj^+zk^ To find ∫∫SF.dS: The divergence theorem states that ∫∫SF.dS=∫∫∫V∇.F dV…

Q: Calculate F. dS where F = (e" sin y, e" cos y, yz²) S is the surface of the box bounded by the…

A: We have to find double integral of F. ds

Q: Calculate || F. dS where S F = (3xy?, xe², z*) S is the surface of the solid bounded by the cylinder…

A: Use the divergence theorem to compute the surface integral ∫∫SFdSwhere S is the surface of the solid…

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

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Q: Integrate g(x, y, z) = x4y(y2 + z2 ) over the portion of the cylinder y2 + z2 = 25 that lies in the…

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 8x + 16y + 24z on the elipse…

A: To determine the maxima and minima of the function f(x, y, z) with respect to the function is…

Q: please help me as soon as possbile

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Q: E) Sketch the solid bounded by the cylinder ** +y = 4 and the planes y+z = 4 and z = 0

A: Here, we need to sketch the solid bounded by the cylinder x2+y2=4 and the planes y+z=4 and z=0.

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: Calculate F. dS where F = (42*z, 4y°z, 3z*) /25 – x² – y², z : 16 — г? — у? = Z 2 S is the surface…

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Q: Find the surface integral (x + y²)dS when S is the cylinder x² + y² = 4,0 < z < 5.

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Q: Evaluate the surface integral fSs x dS, where S is the cylinder y²+z² = 4 between (2) the planes x =…

A: We have to evaluate the surface integral

Q: Evaluate the surface integral (4x² + 3y)dS where S is the part of the plane 2.x + 5y + z = 48 inside…

A: We need to calculate:∬S4x2+3ydS over the surface S,which is the part of plane 2x+5y+z=48, inside the…

Q: Express the volume of the solid that lies between two cylinders a² + y2 = 1 and ² + y² = 4 and…

A: Consider the given equation of the cylinders, x2+y2=1x2+y2=4 and the paraboloid, z=9-x2-y2. In the…

Q: Calculate / F . dS where F = (e* sin y, e cos Y, yz²) S is the surface of the box bounded by the…

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Q: Find SS F dS where F(x, y, z) = z i+(3x – 1)j+ yk and S is the portion of the plane x + y + z = 1…

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Q: Evaluate the surface integral. || x2yz ds, s is the part of the plane z = 1+ 2x + 3y that lies above…

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