#5. Use Stokes' Theorem to evaluate curl F· dS, where F(x,y,z)= x (sin z)i+ y²j+xyk and S is the part of the paraboloid z = 1-x² – y? that lies above the xy-plane, oriented upward.

Q: In Exercises use the surface integral in Stokes' Theorem to calculate the circulation of the field F…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: O) Use Stokes' Theorem to evaluate F. dr where F(x, y, z) = xyi + j + xyk and C is the curve of…

A: (c) The curve, C can be easily parametrized using the following parametrization: x=cos t, y=sin t…

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: use the curl integral in Stokes’ Theorem to find the circulation of the field F around the curve C…

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Q: 4. Confirm Stokes' theorem for the vector field F(x.y.z)= (0, yz, xz) for the plane surface z =1-y…

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Q: Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = ze'i + x cos(y)j + xz sin(y)k, S is the…

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Q: Let a, b > 0. Verify Stokes' Theorem f F - dĩ = SS, curl(F) - ndS for 2xz the vector field F(x, Y,…

A: Let a, b>0. Verify Stokes' Theorem ∮F→· dr→ =∫∫σ curl F→. n dS for the vector field F→x, y,…

Q: Evaluate the line integral ∮C F ⋅ dr using Stokes’ Theorem. Assume C has counterclockwise…

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Q: Let F < xy, 6z, 3y Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of…

A: The given problem is to evaluate the line integral using stokes theorem, we have to find the limits…

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: Use the Stokes' Theorem to caleulate the circulation of the field F = -6y*7 + 6x*J° + 7z*R° around…

A: Given field, F→=-6y3i^+6x3j^+7z3k^ where C is the curve of the paraboloid x2+y2=z cut by the…

Q: Suppose C is the curve parametrized by 7(t) = (cost, sin t, 1) and S is the portion of z = * + y…

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Q: 339. Use Stokes' theorem to evaluate curl F · dS, where F(x, y, z) = e®Ycos zi + æ²zj+ xyk, and S is…

A: please see the next step for solution

Q: How can I verify Stokes' Theorem in the problem?

A: Stokes Theorem: we want to verify stokes theorem.Let, Given:

Q: Use Stokes' Theorem to evaluate || curl F. dS. F(x, y, z) = x² sin(z)i + y²j + xyk, S is the part of…

A: Here use the stokes theorem to find the integral of the function and given that the function…

Q: Use Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = x2z2i + y2z²j + xyzk, S is the part of the…

A: Given: F(x,y,z)=x2z2i+y2z2j+xyzk   and S is the part of the paraboloid z=x2+y2 that lies inside the…

Q: 14. Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field: (r…

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Q: Jse Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = x2 sin(z)i + y?j + xyk, S is the part of…

A: Consider the vector field F⟨x,y,z⟩=x2sinzi+y2j+xyk S is the surface which is part of the…

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: Use Stokes' Theorem to evaluate ∫∫ s  curl F. dS  F(x,y,z) = x2 sin zi +y2 j +xyK, S is the part of…

A: Given: F(x,y,z)=x2 sin z i + y2 j +xy k and S is the surface of paraboloid z=1-x2-y2, which is above…

Q: Use Stokes' Theorem to evaluate      Scurl F · dS. F(x, y, z) = x2 sin(z)i + y2j + xyk, S is the…

A: Given: F(x,y,z)=x2sinzi+y2j+xyk s is part of paraboloid z=1-x2-y2 that lies abovext plane i.e z=0

Q: Q2. Use the Stokes' Theorem to find fF.dr where F(x,y,z) = and C z=9-x²-y² on the xy plane oriented…

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Q: Evaluate the surface integal [[Curl F.ñ dS for the Sur face and F=xt-y²+ (x+4+z)Ñ and C is the bo…

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Q: 4. Use Stokes' Theorem to evaluate curl F · dS when F = ze i+ x cos yj+ xz sin y k and S is the…

A: Given : F = zeyi + x cos y j + xz sin y k and Sis the hemisphere x2 + y2 + z2 = 16, y ≥ 0.   To…

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: 3. Use the surface integral is Stokes' Theorem to calculate the flux of the curl of the field F…

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Q: Use Stokes' Theorem to evaluate curl F. dS. F(x, y, z) = x2y3zi + sin(xyz)j + xyzk, S is the part of…

A: Stokes theorem: ∫∫ScurlF.dS=∫CF.dr

Q: Use Stokes' Theorem to evaluate |/ curl F. dS. F(x, y, z) = tan-(x²yz²)i + x²yj + x²z?k, S is the…

A: Stokes' Theorem:                                 ∮C F .dr =∬S curl F. dS Where C is the boundary of…

Q: 9) Use Stokes' Theorem to evaluate || curl (F)· dS where F(x, y, z) = (x sin z)i+(x)j+(xy)k and S is…

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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: Use Stokes' theorem to evaluate |/ curl(F) · ds. F(x, y, z) = x? sin(2) i + y?j + xyk, S is the part…

A: Use the formula of Stokes theorem and use the parameterization of curves to determine the values of…

Q: Use Stokes' theorem to evaluate f curlF · ds. F(x, y, z) = y²zi+xzj + x²y²k S is the part of the…

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Q: Use Stokes' Theorem to evaluate SSs curl F· dS. F(x,y,z) = x2z2 i + y²z² j + xyz k S is the part of…

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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: Use Stokes theorem to evaluate ff.curl F.nds. where F = (xyz, x, e* cos z), while S is surface x² +…

A: Solution :

Q: Use Stokes' Theorem to evaluate curl F- dS where F(x, y, z)=x²yi+cos¬x² +y]j+4yzk and S 1s the cone…

A: The given function, F(x,y,z)=x2yi+cos-1(x2+y)j+4yzk To find Curl F: F=Pi+Qj+Rk Using Stokes'…

Q: 2. When F = (y z, xz, x² y?) and S is the part of the paraboloid z = x? + y? that lies in the…

A: First, we have to parametrize the surface to apply the Stokes theorem.  Part of the paraboloid is…

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: Given F(x, y, z) = -xị + yzj + xyzk be a vector function that passes through a surface S of z+x² +…

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Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F= 3yi +…

A: Given, F→=3yi^+5-3xj^+z2-2k^r→=3sinφcosθi^+3sinφsinθj^+3cosφk^ So, the flux of curl F is, Flux of…

Q: Use Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = x² sin(z)i + y²j + xyk, S is the part of…

A: Given problem is :

Q: se Stokes's Theorem to calculate (curl F) · n dS . 14) F = -2x2yi + 2xy²j + z°k; S is the portion of…

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Q: Use Stokes' theorem to evaluate curl(F) · ds. F(x, y, z) = exYi + ej + xzk, Sis the half of the…

A: Given: F(x,y,z)=e4xy i+exz j+x2z k The half of ellipsoid 8x2+y2+8z2=8 To find:  ∫S∫curl(F). dS Use…

Q: 1. Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around…

A: We can solve this using Stoke theorem

Q: use the curl integral in Stokes’ Theorem to find the circulation of the field F around the curve C…

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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: 7. Use Stokes Theorem to evaluate I curl F ds F = (x, y, z) = z²i+ 2xj + y2k, S:z = 1- x² - y²,z > 0

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Q: Define stokes theorem and evaluate the line integral SF.r'(s) ds where F = [4z, 2x, 2x], C: the…

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Q: Use Stokes' Theorem to Calculate . curl F.ds F (x, y,z) = x*y³ zî+ Sin (xyz)j + xyz k where o is the…

A: Consider the provided question, F→x,y,z=x2y3zi^+sinxyzj^+xyzk^ that lies between the planes y = 0…

Q: Use Stokes' Theorem to evaluate|| curl F. dS. F(x, y, z) = x²y³zi + sin(xyz)j + xyzk, S is the part…

A: The vector field is Fx, y, z=x2y3zi+sinxyzj+xyzk Find: ∫∫Scurl F·dS Then, the double integral…