Suppose that C is the curve of interesection between the plane z = x and the cylinder x² + y? 1 (an ellipse), oriented counterclockwise when viewed from above. Let S be the interior of this ellipse, oriented with an upward pointing normal vector. If F(x, y, z) = xi+ zj+ 2y k, verify Stokes' theorem by showing that F. dr = curl F· dS S

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

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Q: 11. If F= (y? +z? - x²) î + (z² + x² – y²)j+(x² + y² – z²) k, evaluate fcurl F-î ds integrated over…

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Q: Let C be the curve intersection of the sphere x'+y+=9 and the cylinderx+y° =5 above the xy-plane,…

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Q: Use Stokes' Theorem to evaluate SSs curlF · dS, where F(x, y, z) = 7xyi + 3yzj+4z²k and S is the…

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

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Q: Suppose that C is the curve of interesection between the plane z = x and the cylinder x² + y? be the…

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Q: Suppose F(r, y) = (e", e") and C is the portion of the ellipse centered at the origin from the point…

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

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Q: Use Stokes's theorem to evaluate F.dr, where F(r, y, z) = ry i + x°yj+yz k, where C is a triangular…

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Q: Use Stokes' theorem to evaluate $ (xy – y) i – In z j+ (x +x²) k) • dr, where C is the intersection…

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Q: Let F . F. dr, where Use Stokes' Theorem to evaluate C is the curve of intersection of the…

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Q: Let F = Use Stokes' Theorem to evaluate F. dī, where C is the curve of intersection of the…

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Q: Let C be the curve of intersection between the ellipsoid x?+2y?+3z2=1 and the plane z-x. Let m be…

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Q: Let ~F = (−xy + xz2)~i + (4xz + y2)~j + ez ~k. Use Stokes’ Theorem to calculate ∫C ~F ·d~r, where C…

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Q: Given F(x, y, z) = -yzį + xzj – xyzk be a vector function that passes through a surface S of z +x? +…

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Q: b) Use Stokes' Theorem to evaluate fF•dr for F(x,y,z) =-yi+ xz j+ zk where C is the curve of…

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Q: #6. Use Stokes' Theorem to evaluate S. F dr, where F(x, y,2) = i+(x + yz)j+(xy-V) k and C is the…

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Q: 1. Use Stokes' Theorem to evaluate curlF.dS where F =z'i+ (4y-y) j+2zk and S is the portion of z = r…

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Q: Use Stokes's theorem to evaluate F dr, where F(r, y, z) = ry i+x*yj+yz k, where C is a triangular…

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Q: (a) ( Evaluate the integral zdV where E is enclosed by the paraboloid z = x² + y? and the plane z =…

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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 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…