18. Let S be the portion of the plane z = x contained in the half-cylinder of radius R depicted in Figure 17. Use Stokes' Theorem to calculate the circulation of F = (z, x, y + 2z) around the boundary of S (a half-ellipse) in the counterclockwise direction when viewed from above. Hint: Show that curl(F) is orthogonal to the normal vector to the plane. -R y R FIGURE 17

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