10. Use Stokes's Theorem to evaluate, ?_C z dx + x dy + y dz, Where C is the trace of the cylinder x^2 + y^2 = 1 in the plane y + z = 2 oriented in the counterclockwise direction.
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First, we need to find a surface S whose boundary is the given curve C. A natural choice is the disk x^2 + y^2 ≤ 1 in the plane y + 2 = 2, or equivalently, y = 0. Show more…
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