Suppose that C is the curve of interesection between the plane z = x and the cylinder x² + y? 1 (an ellipse), oriented counterclockwise when viewed from above. Let S be the interior of this ellipse, oriented with an upward pointing normal vector. If F(x, y, z) = xi+ zj+ 2y k, verify Stokes' theorem by showing that F. dr = curl F· dS S

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