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the centroid

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Please help me with the following calculus problems:
1) Set up (do not integrate) an integral for the length of the curve y=tan-1x for x E [0,π).
2) Find the surface area obtained by rotating the curve x=2-y2 around the y axis.
3) Find the centroid of the region bounded by the curve x=2-y2 and the y axis.

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In this solution, we explain how to determine the length of the given curve.

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