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verify Stokes' thm.Assume that the surface S is oriented upward F = 2zi - 3xj +...

verify Stokes' thm.Assume that the surface S is oriented upward F = 2zi - 3xj + 4yk ; S that portion of the paraboloid z =16 - x2- y2 for z>=0. My primary is how to convert dS into dA

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Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed...
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = (x + y2)i + (y + z2)j + (z + x2)k, C is the triangle with vertices (7, 0, 0), (0, 7, 0), and (0, 0, 7).
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed...
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Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed...
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1A) Let S be the upward oriented surface of the box [-pi,pi]x[0,pi]x[0,pi]without the face xy plane....
1A) Let S be the upward oriented surface of the box [-pi,pi]x[0,pi]x[0,pi]without the face xy plane. That is, in the standard view, the box has a front and back, a left and right face, a top face, but no bottom face. Let F(x,y,z)=< ycos(z),zcos(x),xcos(y) >. Find the flux of curl F across S directly,  without using stokes theorem. 1B)  Let S be the upward oriented surface of the box [-pi,pi]x[0,pi]x[0,pi]without the face xy plane. That is, in the standard view, the box...
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Evaluate the surface integral    S F · dS for the given vector field F and...
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Evaluate the surface integral    S F · dS for the given vector field F and...
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Evaluate the surface integral    S F · dS  for the given vector field F and the...
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