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

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

F(x, y, z)= exy cos zi + x2zj + xyk, S is the hemisphere x = √1 – y2 – z2, oriented in the direction of the positive x-axis 


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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