Question: Verify Green's Theorem for the line integral (oint_{C} x y d x+y d y), where (C) is the unit circle, oriented counterclockwise. THEOREM 1 Green's

Verify Green's Theorem for the line integral $\oint_{C} x y d x+y d y$, where $C$ is the unit circle, oriented counterclockwise.

THEOREM 1 Green's Theorem Let D be a domain whose boundary ID

THEOREM 1 Green's Theorem Let D be a domain whose boundary ID is a simple closed curve, oriented counterclockwise. If F and F2 have continuous partial deriva- tives in an open region containing D, then II (3-3) da dA & Fidx + Fdy = = 2

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