Question: Verify that Stokes Theorem is true for the given vector field F and surface S. F(x, y, z) = y 2 i + xj +

Verify that Stokes Theorem is true for the given vector field F and surface S.

F(x, y, z) = y2i + xj + z2k, S is the part of the paraboloid z = x2 + y2 that lies below the plane z = 1, 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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