Calculate the line integral of the vector field ?=〈?,?,?2+?2〉F=〈y,x,x2+y2〉 around the boundary curve, the curl of the vector field, and the surface integral of the curl of the vector field.
The surface S is the upper hemisphere
?2+?2+?2=36, ?≥0x2+y2+z2=36, z≥0
oriented with an upward‑pointing normal.
(Use symbolic notation and fractions where needed.)
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