63. Verify Stokes' theorem for A = (y - z +2)i + (yz +4)j – xz k, where S is the surface of the cube x= 0, y = 0, z = 0, x = 2, y = 2, z = 2 above the xy plane. Ans. common value = - 4

Q: Let C be the curve y 6x° for 0 < a < 1.9. 40+ 36- 32 28- 24 - 20- 16- 12- 8- 0.5 1.5 Find the…

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Q: 3. Use Stokes' theorem to evaluate the integral F. dr where C is the curve given by the intersection…

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Q: If A = 2yz i - (x +3y - 2)j + (x²+z)k, evaluate |(V×A) •n dS over the surface of intersection of the…

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Q: 4. Use Stokes’ theorem to evaluate fa F. dr, where F(x,y, z) = (xy,yz, zx), and C is the triangle…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 11. Find the area of the surface obtained by rotating the curve y = a, 0 < a < 3/4, about the a…

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Q: 3) Evaluate the surface integral. I| (x²z+ y²z) ds where S is the part of the plane z = 4 + x +y…

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Q: Verify Stokes' theorem for F = (x+y-4) i+3xy j+ )k, over the surface of the hemisphere x2 + y2 + z2…

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Q: Q2) Evaluate each side of Stokes theorem for a portion of sphere :r=2m, O=t/3, 0<¢<a H= 2r cosO sino…

A: This question is about application of Stokes theorem

Q: 5) Consider the surface S shown in the graph, whose parametrization is given by by: r(u, v) = (v²,…

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Q: 1. Verify Stokes' Theorem for F = (2x - y)i - yz²j - y² zk, where S is the upper half surface of the…

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Q: 1. What is the differential for the total surface area of a frustum of a cone with l as the slant…

A: Given slant height l. Let r and R be the radii of the frustum. Let h be the height of the frustum.…

Q: I = y dx + (z — х) dy — ydz, Jc

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Q: Q2) Evaluate each side of Stokes theorem for a portion of sphere :r=2m, e= T/3, 0<¢<a H= 2r cosO…

A: This question is about application of stkoes theorem

Q: Q#5. Evaluate the surface integral ff(x,y,z)dS When f(x, y, z)= 3xyz and is the portion of the plane…

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Q: 1 Find the area of the surface obtained by rotating the curve y = In(1 – x²), 0 < x <. about the

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Q: 3.) Verify the conclusion of Stokes' Theorem given F(x,y,z)=(x-y,y-z,z–x) where S is the surface cut…

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Q: Verify Stokes' Theorem for F(x, y,z)= (y,-x, yz) and S is the paraboloid z = x² + y° , 0<zsl. Assume…

A: ∫F→.dr→=∫∫Scurl F.n dA.Here  Fx,y,z=y1-x1 yzS  is the parabloid  Z=x2+y2, 0≤Z≤1

Q: 2) Using Stokes theorem, evaluate pvdr where v= 2y'i– 2x° j+÷k_and the C is the curve of C…

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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: Use Stokes' theorem to evaluate      CF · dr  where C is oriented counterclockwise as viewed from…

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Q: 6. Use Stokes theorem to evaluate $. F•dr, where F = (-3y² , 4z, 6x) and C is the triangle in the…

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Q: 18 Verify Stokes' theorem F.dr = (curl F)· dS C S where F = (x² + y – 4, 3xy, 2xz +z?) and S is the…

A: We have

Q: 2/ MATH

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Q: 10. Use Stokes' Theorem to evaluate ||(V×F)· dS where F= (z,2x, y) and Sis the hemisphere of x' + y?…

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Q: (b) Verify Stokes' theorem on a region which is a portion of the sphere x? +y? +z² = 16 which lies…

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Q: Attached picture is the question

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Q: Use Stokes' theorem to evaluate      CF · dr  where C is oriented counterclockwise as viewed from…

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Q: Q#5. Evaluate the surface integral When f(x, y, z) = 3xyz and o is the portion of the plane x + 3y +…

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Q: Verify Stokes' Theorem for F(x, y, z) = (y,-x, yz) and Sis 13.) the paraboloid z = x² + y², 0≤z≤1.…

A: Let S be a open surface bounded by a closed curve C and F=f1i^+f2j^+f3k^ be a continuous…

Q: 18 Verify Stokes' theorem F dr (curl F) · dS C where F = (x² + y – 4, 3xy, 2xz + z²) and S is the…

A: The complete solutions are given below

Q: S,F•dr, and C is the triangle, with Use Stokes Theorem to evaluate where F(x,y; =) = (x+ y² )i+ (vy+…

A: Given: Fx,y,z=(x+y2)i+y+z2j+z+x2k and C is the triangle with vertices 1,0,0 ,0,1,0 and 0,0,1 We know…

Q: 11. Let F = (-xy + xz²)i + (4xz + y²)j + e² k. Use Stokes' Theorem to calculate fcF. dr, where C is…

A: We have to find∫cF→.dr→.

Q: (ii) Use Stokes' Theorem to evaluate SF · dr, where F(x, y, z) = x²zi+xy²j+z²k and C is the curve of…

A: Given function is F(x,y,z)=x2z i^+xy2 j^ +z2k^ . Plane: x+y+z=1 Cylinder: x2+y2=9 The objective is…

Q: :) Use Stokes' theorem to evaluate RF dr where C F = z?i + yj + xk and C is the triangle with…

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Q: 4) Use Stokes theorem to evaluate SF.dr, where с F(x, y, z) = <.xy, yz, *x), where C is the triangle…

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Q: 3) Use Stokes theorem to evaluate (| curl F-ndS. where F= (xyz, x, e" cos z), while S is a surface…

A: r(t) is the vector function for C, the curve around the base of the hemisphere (and therefore the…

Q: 1. Find the surface area of the cone z = Jx2 + y2 that lies between the plane y = x and the cylinder…

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Q: Use Stokes' Theorem to evaluate L* + cos x) dx + (sin y + z²) dy + x dz where C is the closed curve…

A: To Evaluate: Use Stoke's Theorem:

Q: - Prove Stokes' Theorem by verifying it for F= [y,z,x] and S the paraboloid. %3D te CEY2=(x, y) = 1…

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Q: 5. Use Stokes theorem to evaluate J[V x F-ds over the surface of the paraboloid z = 5-x² - y² above…

A: If S  be   smooth surface bounded by a  closed , positively  oriented  smooth boundary curve C with…

Q: Verify Stokes' theorem for A = (p a, + cos o a, + a:) on the upper half-surface of the sphere x + y?…

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Q: 3. Suppose F z = 4 – a? – y? above the r- y plane, oriented upward. Calculate fe F dĩ in two ways:…

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Q: Let ~F = (−xy + xz2)~i + (4xz + y2)~j + ez ~k. Use Stokes’ Theorem to calculate ∫C ~F ·d~r, where C…

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Q: 11. Consider F(x, y, z) = (-y, x, e²) and the surface defined by S = {(x, y, z) : z =1– 2² – y², x²…

A: Given F=-y,x,ez and S=x,y,z| z=1-x2-y2,x2+y2≤1. Verify the stokes theorem ∫CF·dr→=∬Scurl F·n→ dS.

Q: Use Stokes's Theorem to show that 0= [[ curl(F) - dS where F(r, Y, z) = (2, 2ry, x + y) and S is the…

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Q: 1. Use Stokes' Theorem to evaluate curlF.dS where F =z'i+ (4y-y) j+2zk and S is the portion of z = r…

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Q: iv) Given F (x, y, z) = -yzį + 2xj + xyzk be a vector function that passes through a surface S of z+…

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Q: 4. Use Stokes' Theorem to evaluate |F• dr when F(x, y, z)= z' i+y° j+xy k. Let S is the part of the…

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