Question: Use Stokes Theorem to evaluate S curl F ds.k F(x, y, z) = 2y cos zi + e x sin zj + xe

Use Stokes Theorem to evaluate ∫∫S curl F · ds.k

F(x, y, z) = 2y cos zi + exsin zj + xey k, S is the hemisphere x2 + y2 + z2 = 9, z ≥ 0, 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

S F dr = ff S curl F. ds

S F dr = ff S curl F. dS

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