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Math Help - Stokes Theorem Help Needed!

  1. #1
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    Stokes Theorem Help Needed!

    Use Stokes' Theorem to evaluate

     \int  F \cdot dr  C\ is\ oriented\ counterclockwise\ as\ viewed\ from\ above.
     F(x,y,z) = x i + y j + (x^2 + y^2) k
     C\ is\ the\ boundary\ of\ the\ part\ of\ the\ paraboloid\ z = 1 - x^2 - y^2 in\ the\ first\ octant\

    C is the boundary of the part of the paraboloid  z = 1-x^2-y^2  in the first octant.


    The formula for stoke's theorem is  \int F \cdot dr = \int\int curl \cdot dS

    I went ahead and found the curl which is (2y-2x)k. So, when i set up the double integral, so far i have  \int\int (2y-2x)dA

    However, im having trouble with figuring out the bounds. I think this is a sphere, so does that mean i have to use spherical coordinates? Is there a simpler way because im really not good with spherical coordinates! Thanks.
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  2. #2
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    Sorry to bump, but i need help with this promblem within an hour! All suggestions would be appreciated .
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