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 the piece of the paraboloid z = 4-x – y? that lies above the xy-plane, oriented upward.

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

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Q: 2. Verify the Stokes's Theorem for the calculation of the work done by the vector field: F = (r,y²,…

A: Stokes theorem is verified

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

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Q: In Exercises 39 and 40, use the surface integral in Stokes' Theorem to find the circulation of the…

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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 frotF. ds. F(x, y, z) = xyi + e²j + xy²k; S consists of the four…

A: To find- Use Stokes' theorem to evaluate ∫SrotF·dS, Fx, y, z = xyi + e2j + xy2k; S consists of the…

Q: 3- Use Stokes theorem to compute the line integral F . dr, where F = [e-3y, e, e201 and C is the…

A: By using the stokes theorem we need to find ∫CF·dr, where F=e-3y, ez, e-2x and C is the boundary of…

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: 9. Use Stokes' Theorem to evaluate F. dr where F(z, y, 2) = (2 – y) i + (x + 2)j – (x + y) k and C…

A: The given problem is to evalute the contour integral using stokes theorem, where surface C is the…

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = (y² +z²)i…

A: To calculate the circulation of the field F=y2+z2i+x2+y2j+x2+y2k around the curve C: The square…

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: Use Stokes' Theorem to evaluate F. dr where F(x, y, z) = xi + yj +Xx² + y² )k and C is the boundary…

A: Stokes theorem: ∮f→·dr→=∬S curl f→·n^ ds Given F(x, y, z)=xi + yj+9(x2+y2)k and C is the boundary of…

Q: #5. Use Stokes' Theorem to evaluate curl F· dS, where F(x,y,z)= x (sin z)i+ y²j+xyk and S is the…

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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) = zeYi + x cos(y)j + xz sin(y)k, S is the…

A:

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: 4) Evaluate the surface integral [[F•dS where F(x,y,z)= (yz,-xz,z)and S is the piece of the…

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Q: Use Stokes' theorem to evaluate curl F. dS, where F(x, y, z) = e*Y cos(z)i + x²zj + xyk, and S is…

A:

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

A:

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 E (wy – y) i – In z j+ (x+x²) k) · dr, where C is the intersection…

A: The required curve C(red) is shown as follows: The intersection gives a disc D bounded by curve C,…

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 the surface integral is Stokes' Theorem to calculate the flux of the curl of the field F…

A:

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: 14. Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field: F =…

A:

Q: Use Stokes' Theorem to evaluate [[(curlF)•ndS where F(x,y,z) =x’i+z°j-y°k and o is that portion of…

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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…

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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 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: . Evaluate the flux integral f. curl (z cos xi+ yj+ x sin y k) dS where S is the part of the outward…

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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 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: 3- Use Stokes theorem to compute the line integral ScF · dr, where F = [e-3y, e², e-2"] and C is the…

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Q: Use Stokes theorem to evaluate F- dr. where F = (2, 2z, y) and C is the boundary of the paraboloid…

A: Stokes theorem: ∫CF.dr =∫∫Scurl F.N ds Curl F of the vector function F=f1i+f2j+f3k 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: 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: 2). Use Stokes' theorem to evaluate the integral 6 F • dř for F(x, y, z) = (x – y)î + (y – z)ĵ + (z…

A: Formula: By Stoke's theorem we have ∮C F · dr¯  =∫t=t1t=t2 F¯(r(t))r'(t) dt, where r(t) is…

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: 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: 3- Use Stokes theorem to compute the line integral SF· dr, where F = [e-3y, e², e-2*] and C is the…

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Q: Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = xyzi + xyj + x²yzk, S consists of the top…

A: The given problem is to evaluate the surface integral using stokes theorem where S is the surface of…