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...Ma exercise sheet solutions h verify green s theorem in the plane for c xy y dx x dy where is closed curve of region bounded by and solution now i xdy f dr are given figure we parameterise as t then r thus z dt so says zz dxdy dydx question divergence vector eld xi yj zk taken over cylinder rrs ds rrrv fdv zzz v dv use cylindrical co ordinates rcos rsin rdrd dz zr d sin cos calculate rr see b on n k since nds area finally also j rz...