Question: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwse indicated. C x y d x + ( x 2

Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwse indicated.

THEOREM 1 Green's Theorem Let D be a domain whose boundary 3D

$\int_{C} x y d x + (x^{2} + x) d y$ , where $C$ is the path in Figure 17

is a simple closed curve, oriented counterclockwise. If F and F have

THEOREM 1 Green's Theorem Let D be a domain whose boundary 3D is a simple closed curve, oriented counterclockwise. If F and F have continuous partial deriva- tives in an open region containing D, then $o F1 dx + F2 dy 1 (F2-F) da dA = ay 2

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