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-   -   Stokes' Theorem (https://www.askmehelpdesk.com/showthread.php?t=292180)

  • Dec 14, 2008, 07:27 PM
    jianjunzhou2008
    Stokes' Theorem
    Use Stokes' Theorem to evaluate http://www.math.umn.edu/~nykamp/m237...sidea/img6.gif
    F(x,y,z)=(x^2)(z^2)i+(y^2)(z^2)j+xyzk, S is the part of the paraboloid z=x^2+y^2 that lies inside the cylinder x^2+y^2=4, oriented upward:confused:
  • Dec 15, 2008, 09:18 AM
    galactus
    Because it is oriented upward, we can parametrize S:





    Now, use those in

    Find your curl F by taking the cross product



    There's a start.

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