Evaluate the surface integral ∫∫fs * ds for the given vector field f and the oriented surface s. in other words, find the flux of f across s. for closed surfaces, use the positive (outward) orientation. f(x, y, z) = x i + y j + 8 ks is the boundary of the region enclosed by the cylinder x^2 + z^2 = 1 and the planes y = 0 and x + y = 6

so that by the divergence theorem,

where is the interior of . In cylindrical coordinates, the integral is

where we set

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