Let S be the portion of the cylinder y = e^x in the first octant that projects parallel to the x-axis onto the rectangle R_yz: 1 ≤ y ≤ 2, 0 ≤ z ≤ 1 in the yz-plane. Let n be the unit vector normal to S that points away from the yz-plane. Find the flux of the field F(x, y, z) = -2i + 2yj + zk across S in the direction of n.

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X Z 1 1- y = ex S Ryz A 2