4. Use Stokes' Theorem to evaluate curl F.dS where F = (x-y, yz, xz) and S is that part of the paraboloid z = 4 x2 y2 where > 0, oriented upwards. - -

Q: Use Stokes' Theorem to evaluate      Scurl F · dS. F(x, y, z) = zeyi + x cos(y)j + xz sin(y)k, S…

A:

Q: Use Stokes' Theorem to evaluate curl F- dS where F(r, y, 2) = 4ryzi – ryj + x?yzk and S consists of…

A:

Q: F(x, y, 2) = 2y cos(2) I+ e sin(2) j + xe k, S is the hemisphere x + y? + 22 = 9, z 2 0, oriented…

A: Surface integration

Q: F · dr  where F  =  (x + 5z) i  +  (7x + y) j  +  (2y − z) k   and C is the curve of intersection of…

A:

Q: Use Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = 4y cos(z) i + e\ sin(z) j + xeY k, S is the…

A:

Q: Find VX A for the vector A given by A = -yax + x ay Evaluate Ad A de around the curve x² + y²2 = 1…

A:

Q: Let F=. •[ f, cu S is the part of the paraboloid z = 10 - x² - y² that lies above the plane z = 9,…

A:

Q: e Il Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = x²z² + y²z²j + xyzk, S is the part of…

A:

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

A:

Q: Let C be the boundary of the portion of the plane x+y+z=2 that lies in the first octant, oriented…

A:

Q: Use Stokes's Theorem to evaluate e curlF. ds. (1) F(x, y, z) = x²y³zi+sin(ryz)j + xyz k, S is the…

A: “Since you have posted multiple questions, we will provide the solution   only to the first question…

Q: F(x, y, z) = tan-'(x?yz²)i + x²yj + x²z?k, S is the cone x = V y2 0 <x < 4, oriented in the…

A: Define curve C with boundary curve: r→=4i^+4costj^+4sintt^

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: •11• F(x, y, z) = xyzi + xyj + x²yzk, S consists of the top and four sides (but not the bottom) of…

A: We have to find the ∫∫curlF ds

Q: 9. If F = (x – z) î + (x³ + yz)ĵ + 3xy² k and S is the surface of the cone z = a – Va? +y?) above…

A:

Q: Given F = (yz,x+y+=,xz), determine curl F .

A: Curl F ( -1, y-z ,1-z)

Q: Given F(x, y, z) = xzi + 3yj + yzk be a vector function that passes through a surface S of z+x² + y?…

A:

Q: - 2 and Evaluate || curl(F)·dS where S is the portion of the top half of the sphere x +y +z? = 4…

A:

Q: Use Stokes' theorem to evaluate ∬S curl(F) · dS. F(x, y, z) = xyz i + xy j + x2yz k,    S consists…

A:

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: a) Find the curl V×Fif F = (y',2xy,yz)

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: F(x, y, z) = yzi + 8xzj + exyk, C is the circle x² + y² = 1, z = 4.

A:

Q: Use Stokes' Theorem (in reverse) to evaluate (curl F) ndS where F = 6yzi + 9xj +6yzeªk,S is the…

A:

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

A: Solution :