Use Green's Theorem to evaluate the line integral around the given closed curve. (oint_{C} y e^{x} d
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Use Green's Theorem to evaluate the line integral around the given closed curve.
\(\oint_{C} y e^{x} d x+x e^{y} d y\), where \(C\) is the triangle with vertices \((-1,0),(0,4)\), and \((0,1)\), oriented counterclockwise
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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 Fi f Fdx + Fdy = = 16 (f/ TL (SF2-F1) a dA D
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