Verify the Divergence theorem for the following surface integral A’. dŠ where A (x,y,z) = x²z³i+ 2xyz³j+ xz*k and S is the surface of the box defined as S = {(x, y, z)| 0 < x<1, 0< y< 2, 0

Q: Use only the Stokes’ theorem to evaluate  integralC(−z − y)dx + (x − z)dy + (x − y)dz where C is the…

A: It is given that  F=-z-y,x-z,x-yand C is the intersection of ; z=x2+y2 and z=y Then,…

Q: Evaluate the surface integral G(x,y,z) do using a parametric description of the surface. 2 2…

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Q: calculate || f(x, y, z) dS for the given surface and function. y = 9 – z?, 0<x < 3, 0 < z < 3; f(x,…

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Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 8 n = 4 (-x¹ + 22x³ -…

A: (a)How large should n be to guarantee that the Trapezoidal Rule approximation  to is accurate to…

Q: The surface integral is rewritten incorrectly. F((x, y)) is incorrect. The tangent vectors T, and T,…

A: We will identify the first error in the given work shown.

Q: (10) Let S be the surface S:= {(x, y, z) E R³: 9x2 + 4y² +2²=1, z 20}. Evaluate the surface integral…

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Q: Calculate the surface integral F. NdS, where F = (-3xz, -4xz, 3yz) and S is the surface with…

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Q: F. dS, where F = ze"Yi – 5ze"j+xyk and S is the surface with upward Evaluate S orientation and…

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Q: Evaluate the surface integral ff G (x, y, z) dS, C where G (x, y, z) = x+y+z, and C is the…

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

A: a  x2+y2=9    0≤y≤2,  x⩾0, z⩾0   S is parametrised by     rθ,y=3 cos ϖ, y, 3 sin θ    θ∈0 π2,   y∈0…

Q: Evaluate the surface integral 1 d.S where o is the portion of the plane z = 4 - 6x – 1y in the first…

A: To find  where  is the portion of the plane  in the first octant

Q: F-dS where 50. Use the Divergence Theorem to calculate the surface integral F S F(x, y, z)=sin(y+z)i…

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Q: b) Given F(r, y, z) = (x³ + cosh z) i+ (2y - 3ry)j – (x² + 4y²z) k. Use %3D Gauss's theorem to…

A: 1. The divergence is an operator, which takes in the vector-valued function defining this vector…

Q: Calculate ff f(x, y, z) dS For Part of the surface x Js f(x, y, z) ds = S - z³, where 0 ≤ x, y ≤…

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Q: 2. Let S be the surface x² + y² = (2-2)², y Evaluate Jl F = (2x+y-xz, -x, -(2 — z)²), choosing a…

A: Using parametrization of the surface S

Q: Calculate the surface integral ſf F. NdS, where F = (-x²z, xz², -yz²) and S is the surface with…

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Q: Let G(x, y, 2)= (1+9xy) and consider a surface S given by the parametrization r(u, v)= lu, u",…

A: Given that, Consider a surface S given by the parametrization  To find: the value surface integral…

Q: 2. Use Gauss' Divergence Theorem to evaluate the surface integral J. F. ds. where F= (1, 1, 2(2² +…

A: The given problem is to evaluate the given surface integral of the vector field over the given…

Q: Evaluate the integral FdS, dS upwards S With F(x, y, z) = (x−y, 2z, y-x),where S is the surface…

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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: 6. Use the divergence theorem to determine the surface integral of the vector function F on the…

A: The given problem is to evaluate the surface integral of the given vector field over the given…

Q: Evaluate the surface integral f(x,y,z) ds using a parametric description of the surface. S 2 2 2…

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Q: Evaluate an area of a surface where the vector that is normal to the surface is defined as; d. Q =…

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Q: 5. (a) Evaluate the surface integral || ²: y²2² dS where o is part of the cone z = Vr + y that lies…

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Q: 8. Let F = xyzi + (y² + 1)ĵ + z³k and S be the surface of the cube 0 < x, y, z < 1. (a) Evaluate the…

A: Given that F→=xyzi→+y2+1j→+z3k→ S be the surface of the cube 0≤x,y,z≤1 Now,…