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jheld
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Homework Statement
verify Stokes's theorem for the given surface and vector field.
S is defined by x^2 + y^2 + z^2 = 4, z <= 4, oriented by downward normal;
F = (2y-z, x + y^2 - z, 4y - 3x)
Homework Equations
double integral over S of the curl F ds = integral over S' of F ds.
The Attempt at a Solution
I calculated the curl F= del operator cross-product F = 5i - 2j - k, feel free to check if you wish.
But in my vector calc book for a similar example, I noticed that they made an upward-pointing normal vector (as it was oriented upward) after del x F. I though del x F was a normal vector--am I wrong? The normal vector they came up with after the del x F (a separate calculation for my knowledge) was very different.
Any hints from where to go from there?