Given F(x, y, z) = xzi + 3yj + yzk be a vector function that passes through a surface S of z+x² + y? = 4 that lies above z 0, which is positively oriented. Sketch the surface S based on the given information, then evaluate f, curl F n ds by using Stokes' Theorem. %3D

Q: Use Stokes' theorem to evaluate the surface integral I of the two-form w = dŋ, with n = (xz+ yz²) dæ…

A: η=(xz+yz2)dx+(sin(y)+z+5x)dy+xyz dzz=13-x2-y2,   z≥9 F→=xz+yz2i+(sin(y)+z+5x)j+xyzk z=9⇒9=13-x2-y2…

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Q: Calculate the surface integral / G(r) dA, where G = (12xz + 36)1/2, the surface S is given by the…

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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: Use Stokes' Theorem to find the work done by the force field F = [z<,2x,2y] on a particle that…

A: The given vector field is  F→=z2,2x,2y From Stoke's Theorem we know that…

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

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Q: Find the flux ofF across the oriented surface S' by evaluating the surface integral F.î dS. F = zî +…

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Q: Consider x=h(y,z) as a parametrized surface in the natural way. Write the equation of the tangent…

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Q: Evaluate the surface integral ∫∫H 2yd S where H is the helicoid (i.e., spiral ramp) given by the…

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Q: Let S be the surface z = 9 − x² − y² above the xy plane. Use Stokes's Theorem to compute [[ curt F…

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Q: Find the value of the integral fs (V x A). da if the vector A = yi + zj + xk and Sis the surface…

A: Given the vector A=yi+zj+xk and S is the surface defined by the paraboloid z=1-x2-y2

Q: Use Stokes's Theorem to evaluate  Integral of the curve from the force vector:  F · dr. or the…

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Q: Verify the formula fF-T ds = [ (curl F) -n ds in Stokes' Theorem by evaluating the line integral and…

A: According to the given information, it is required to verify the stokes theorem.

Q: Evaluate the surface integral. y dS, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

A: Consider the provided question,

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: Consider the vector field F(r, y, z) = (x, y, 6z). Evaluate the surface integral I = [[; F · dS…

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Q: Evaluate Curlv-ñ, where v = 2xyi + (x-2y)j+xzk and ñ is a unit vector normal to the surface shown in…

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Q: Given the vector field F = (z, x, y), calculate the flux of the curl of F through the portion of the…

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Q: Evaluate the surface integral. J[x²³x² x²yz ds, S is the part of the plane z = 1 + 2x + 3y that lies…

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Q: Use Stokes' Theorem to evaluate F. dr where F(x, y, 2)æzî + 2ry} +3ryk where C is the boundary of…

A: According to the given information, it is required to use stokes theorem to evaluate the integral.

Q: Q3 Evaluate Curlv-ñ , where v=2xyi +(x -2y)j+xzk and ñ is a unit vector normal to the surface shown…

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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: Evaluate Curlv•ñ , where v = 2xyi + (x² – 2 y)] + xzk and ñ is a unit vector normal to the surface…

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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…

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Q: Q3 Evaluate Curlv•n , where i = 2xyi + (x – 2y)j+xzk and i is a unit vector normal to the surface…

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Q: Calculate the surface integral // y ds, where S is the part of the helicoid defined by the S vector…

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Q: Evaluate Curlv.ñ , where v = 2xyi +(x² – 2y)j + xzk and ñ is a unit vector normal to the surface…

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

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Q: Evaluate the surface integral f(r, y, z)dS,

A: answer is in next step

Q: Evaluate the surface integral. y ds, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

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

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Q: Evaluate the surface integral. y ds, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

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Q: Evaluate the surface integral [[ (a² + y²) dS where S is the surface with vector function r(u, v) =…

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

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Q: Evaluate the surface integral. y ds, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

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Q: Calculate the flux integral f(2i + 2j + 2k) · dA where S is a disk of radius 5 in the plane æ + y +…

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Q: Verify Stokes' Theorem if F(x, y, z) = (x – y)i + (y – z)j+ (z – x)k and S be the portion of the…

A: Solution: The objective is to verify the Stokes theorem for the given problem

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Q: Let S be a square plate with boundary C having length of each side as 2 units, lying in the plane z…

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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: Evaluate the surface integral. V1 + x2 + y2 dS S is the helicoid with vector equation r(u, v) = u…

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Q: Find the area of the surface. The helicoid (or spiral ramp) with vector equation r(u, v) = u cos(v)…

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Q: (4) Use Stokes' Theorem to calculate the work-done by the force field F(r, y, z) = (x² + z²)î + (y²…

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S S is the part of the paraboloid z = 9…

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Q: Use Stokes' Theorem to evaluate , (x + y )dx + (2x – 3)dy + (y + z)dz over the boundary of the…

A: First we will learn about Stokes theorem little bit. If "F1 i + F2 j + F3 k" is a differentiable…

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: 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) = 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…