Question: Let A be the area and x the x-coordinate of the centroid of a region R that is bounded by a piecewise smooth, simple closed

Let A be the area and x̄ the x-coordinate of the centroid of a region R that is bounded by a piecewise smooth, simple closed curve C in the xy-plane. Show that 2 1 f x d y = -xy dx C C 3

2 1 f x d y = -xy dx C C 3 C x dy - xy dx = AX.

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