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...Problems extended stokes theorem let f xz y yz x use to compute dr where c is the curve shown on surface of circular cylinder radius figure positively oriented around a answer this very similar an earlier example we can calculate integral even though don t have exact description just make into part boundary as in gure below curves and bound be unit circle xy plane match s portion between then says curlf n ds i j k z since normal vector always orthogonal thus cf nish parametrize by cos sin...