Use Stokes Theorem to evaluate ∫_C F · dr. In each case C is oriented counterclockwise as viewed from above.

F(x, y, z) = e^–xi + e^xj + e^zk, C is the boundary of the part of the plane 2x + y + 2z = 2 in the first octant

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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S₁ F • dr = ff S curl F. ds