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

\(\oint_{C} e^{2 x+y} d x+e^{-y} d y\), where \(C\) is the triangle with vertices \((0,0),(1,0)\), and \((1,1)\)

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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