Evaluate the surface integral s f · 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 + 9 k s is the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 8

is a closed surface with interior , so you can use the divergence theorem.

By the divergence theorem, the flux of across is given by the integral of over :

Convert to cylindrical coordinates, setting

The integral is then

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step-by-step explanation: