Jse Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = x2 sin(z)i + y?j + xyk, S is the part of the paraboloid z = 9 – x2 - y² that lies above the xy-plane, oriented upward. %3!

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

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

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Q: 2. Verify Stokes's Theorem for F(x, y, z) = y i+ z j +x k and the plane x + y + z = 2 in the first…

A: Given, Fx,y,z=yi^+zj^+xk^x+y+z=2 So, curl F is calculating by, Curl F→=∇→×F→Curl…

Q: Verify Stokes's Theorem for F = z?i + x²j + y?k and S is the surface z? = x² + y?, y 2 0, %3D and 0…

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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: Given that Fx,y,z=4ycoszi+exsinzj+xeyk and S is the hemisphere x2+y2+z2=9,z≥0. The expression for…

Q: Use Stokes' Theorem to evaluate F. dr. F(x, y, z) = z²i + 32xj – y°k - where C is the circle x? + y?…

A: Given Fx,y,z=z2i+32xj-y3k. Let C be the circle x2+y2=1 in the xy plane with counterclockwise…

Q: use the surface integral in Stokes’ Theorem to calculate the circulation of the field F around the…

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Q: b) C is the circle of radius a centred on the origin, oriented clockwise. Use Green's Theorem to…

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Q: curl F • ÑdS, where & is that part of the sphere 8, EXAMPLE Find I = x? + y? + (z – 2)² = 8 that…

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Q: F(x, y, z) = 3yi + 2zj – xk; C is the triangle with vertices %3D (1, 0, 0), (0, 1, 0), and (0, 0,…

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Q: Use Stokes' theorem to evaluate curl(F) · dS. F(x, y, z) = exy cos(z)i + x2zj + xy k, S is the…

A: F(x, y, z) = exy cos (z) i + x2 z j + xy k

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: curl(F) N dS, where (x, y, 2) = -y(a² + y³)2021 î + In(z +1)e*y² }+ z2021 V²+ y? k and S is the…

A: Given,  F^(x,y,z)=-y(x2+y2)2021i^+ln(z+1)ez2y2j^+z2021x2+y2k^and S is the portion of the surface…

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

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Q: Jse Stokes' theorem to evaluate F. dr where Cis oriented counterclockwise as viewed from F(x, y, z)…

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

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Q: Use Stokes' Theorem to calculate the integral / curl F · dà where F = -5yi+ 5xj + (xy+4 cos z)k and…

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Q: CurlF dS x+y' +z =9, z20 se Stokes' Theorem to compute s for the hemisphere intersected with the xy-…

A:

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 surface integral in Stokes' Theorem to calculate the circulation of the field F around the…

A:

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

A: Given The given vector field is F=yi+xzj+x2k and the surface is 8x+y+z=8. Apply formula…

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

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

Q: Using Green’s theorem, evaluate the line integral ∮Cxydx+ (x+y)dy, where C is the curve bounding the…

A: Given: Where the components of the vector field are

Q: Find the surface integral of the field F(x,y,z)=9xi +9yj +9zk across the portion of the sphere x² +…

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Q: Let S be the part of the sphere x² + y? + z² = 4 that lies inside the cylinder x? + y? = 1 and above…

A:

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: eff curl(F). ds. F(x, y, z) = x² sin(z)i + y²j + xyk, S is the part of the paraboloid z = 9 - x² -…

A:

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

A: Given that, And he paraboliod is The aim is to find The radius is 3. Take C is x(t)=cos t and…

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: Use Stokes' Theorem to find curl F · dš, where F(x, y, z) = (xz, -yz, xy) and the S surface S is the…

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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: evaluate ∬s curl F*dS F(x,y,z)=x2sinz i+y2j+xyk S is part of the parabaloid z=1-x2-y2 that lies…

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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 S curl(F) · dS. F(x, y, z) = exy cos(z) i + x2z j + xy k, S…

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Q: Use Stokes' Theorem to evaluate  curl F · dS. F(x, y, z) = 6y cos(z) i + ex sin(z) j + xey k, S is…

A: From the given statement,

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

A:

Q: curl(F) N dS, where F(x, y, 2) = -y(x² + y²)2021 î + In(z +1)e²*y² }+ 22021 vx² + y² k and S is the…

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

A:

Q: Find the surface integral of the field F(x,y,z) = 6zk across the portion of the sphere x +y +z = a…

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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: 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 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…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.