Evaluate [F d$ for F = yi+=j+2xk and S is a surface of the region bounded by the cylinder x+ y = 4 between the planes = = 0 and = 3 in the first octant. %3D Hence, sketch the surface S.

Q: Use Green's theorem to find the surface integral of the following geometry if V = xy'i - x³yi, and…

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Q: Evaluate the surface integral F. ds where F = 5xyi +8x²j+ 5yzk and S is the surface z = ïe², 0 ≤ x ≤…

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Q: Evaluate the surface integral. xz ds, S is the part of the plane 2x + 2y + z = 4 that lies in the…

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Q: Evaluate the surface integral DOUBLE INTERGAL of S −→F . d−→S , where S is the part of the cone z…

A: Given a vector field Fx,y,z=xi^+yj^+z4k^.  Now the surface integral for the vector field in the…

Q: Let C be a simple closed smooth curve in the plane 2x + 2y + z = 2, oriented as shown here. Show…

A: Given, The equation of the curve is 2x+2y+z=2. The closed integral is ∮C2y dx+3zdy-x dz Let…

Q: Find the v o l um e generated by rotating the region bounded by the curves y = ex, x = 0, y = pi abo…

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Q: Evaluate the surface integral F.n dA, where F(x, y, z) = i + j + z(x² + y²)<k and S is the surface…

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Q: 2. Evaluate the surface integral f,yz ds ; o is the part of the plane x + y + z = 2 that lies in the…

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Q: Consider the solid region E inside the sphere x² + y² + z² = 4 and outside the cylinder x² + y² = 1.…

A: This question is based on 3-D geometry.

Q: Evaluate the surface integral (V x F). n ds where S is the portion of the tetrahedron bounded by r…

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Q: Evaluate the surface integral |[(x² + y° \dS_where S is the surface of the paraboloid z = x² + y²,…

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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: Evaluate the surface integral| f(x.y.z) dS using an explicit representation of the surface. f(x.y.z)…

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Q: Evaluate the surface integral. z2 S is the part of the paraboloid x = y2 + z² given by 0 sx 5 4 1 V5…

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Q: Evaluate the surface integral. y ds S is the part of the paraboloid y = x² + z² that lies inside the…

A: The projection of S onto the xz-plane is the disk D=x,z: x2+z2≤9. We have to calculate the surface…

Q: Compute the surface integral over the given oriented surface: F = y²i + 6j − xk, normal F. ds =…

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Q: Find the surface integral ls yz dS, where S is the plane surface z = x + 3y lying above the…

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Q: Evaluate the surface integral. z2 dS, S is the part of the paraboloid  x = y2 + z2  given by  0 ≤…

A: given the surface integral  z2 dS  where S is the part of the paraboloid x= y2+z2   given by 0≤x≤1…

Q: Calculate the surface integral ∫ ∫ s F ∙ N dS where F (x, y, z) = -y2i + xj + k and S is the shaded…

A: We will find out the required surface Integral.

Q: Evaluate the surface integral. y² ds, S is the part of the sphere x² + y² + z² = 1 that lies above…

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Q: Consider the surface S={(x, y, z)| xy+ z= 5; x20; y20; z20} in R3. Use the Method of Lagrange to…

A: The distance between points can be calculated using the distance formula. The distance formula is…

Q: * Evaluate the surface integral SS F - d§, where F = z7 + y²7 + z² and S is the boundary of the…

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Q: Evaluate the surface integral, f(x.y.z) dS using an explicit representation of the surface. f(x.y.z)…

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Q: Evaluate the surface integral: S Ss a?y ds Where S is the surface of the paraboloid z = 4- x2 – y²…

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Q: Evaluate fF.ndS, where F-4xi-2y' j+z'k and S is the surface bounding the region x' +y' =4, and the…

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Q: (a) Evaluate the following surface integral yex²+z² dS, where o is the portion of the surface of the…

A: Given the integral ∬σyex2+z2dS we have evaluate the given surface integral where σ is the portion of…

Q: Evaluate the surface integral: || G(x, y, z) ds for G(x,y,z) = z², where S is the portion of the…

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Q: Evaluate the surface integral of G(x, y, z) = z - y over the surface S, where S is the portion of…

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Q: Consider the surface integral хуdS, where S is the surface z = x² + v8 y for 0 < x < 2 and 0 < y <…

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Q: Choose the correct integral to evaluate the surface integral (x+y)zdS,where S is the portion of the…

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Q: What would be the solution for this question

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Q: lad Use Green's theorem to evaluate y² dx + 3xy dy, where c is the boundary of the semi annular…

A: Given Problem:- Use Green's theorem to evaluate ∮cy2dx+3xydy where c is the boundary of the semi…

Q: 10. Let S be the surface of the solid region above the ry-plane and bounded between the planes x + z…

A: The given curves are x+z=2....(1), -x+z=2...(2),  y=0 and y=3. Also given  F→=z i^+ex j^ +1+yz…

Q: Evaluate the surface integral. z2 ds, S is the part of the paraboloid x = y2 + z? given by 0 < x < 1

A: Evaluate the surface integral.

Q: EX. Find the volune of the solid region lymg mside both the sphere Xtuf+2?= 402 and the cylmeder…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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: Find the surface area of the plane 3x + 2 y + z = 6 that lies in the first octant.

A: The surface area of the plane z=f(x,y) is given by the formula                          S=∬D…

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

A: To evaluate :  ∫∫s(x2 + y2 + z2) dS, S is the part of the cylinder x2 + y2 = 9 between the planes z…

Q: Let S be the piece of the surface z = 9– x2 that lies inside the cylinder x2 +y? = 9, and let F =…

A: According to question, Given Surface, z = 9 -x2 ,This surface lies Inside the cylinder x2 + y2 = 9,F…

Q: Evaluate the surface integral f, F. dS where F = 3xyi + 9x²j+3yzk and S is the surface z = xe", 0≤x≤…

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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: Find the area of the surface z = x² + y? that lies below the plane z = 2.

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Q: Let A = 6 zi + (2x + y)j – x k ; Evaluate A.ndS over the entire surface S of the region bounded by…

A: Please see the figure below to comprehend what's going on:

Q: Consider the surface S which is the part of the cylinder x^2 + z^2 = 9 , whit   0 ≤ y ≤ 2; x ≥ 0; z…

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Q: Evaluate the line integral S.F · dr where F(x,y, z) = x³i – y²j+ zk and C is the poundary of the…

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Q: Evaluate the surface integral [(xz + y* ) ds where s is the surface of the XZ- cylinder y + z? =…

A: Consider the provided question,

Q: f(x) = V4x +1, = V4x + 1, with 1< x < 5

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Q: Evaluate the following surface integrals: (a) x + y) ds, o : part of the surface 2x + 3y + z = 6 in…

A: To calculate the surface integral, first we write the equation of the surface in the form…

Q: The region W lies between the spheres a? + y? + z2 = 9 and æ? + y² + z² = 16 and within the cone z =…

A: Here we can use divergence theorem to find the flux of the vector valued function. Divergence…

Q: For an area A in the x-y plane, the moment of inertia of the element dA about the x-axis is: O dlx =…

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