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:
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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:
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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