[Solution] Prove Green's Theorem for the region in the plane bounded by the x -axis and the curve y=1-x^2 by explicitly computing both sides of the equality


Question: Prove Green's Theorem for the region in the plane bounded by the \(x\) -axis and the curve \(y=1-x^{2}\) by explicitly computing both sides of the equality for a "general" \(P(x, y) d x+Q(x, y) d y\) (be sure to state what conditions on \(P\) and \(Q\) are needed).

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