Use Stokes Theorem to evaluate S curl F ds. F(x, y, z) = x 2
Question:
Use Stokes Theorem to evaluate ∫∫S curl F · ds.
F(x, y, z) = x2z2 i + y2z2j + xyz k, S is the part of the paraboloid z = x2 + y2 that lies inside the cylinder x2 + y2 = 4, oriented upward
Data from Stokes Theorem
Let S be an oriented piecewise-smooth surface that is bounded by a simple, closed, piecewise-smooth boundary curve C with positive orientation. Let F be a vector field whose components have continuous partial derivatives on an open region in R3 that contains S. Then
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