[See Solution] The region in the first quadrant bounded by the graphs of y = x and y = (x^2)/(2) is rotated around the line y = x. Find the centroid of the region


Question: The region in the first quadrant bounded by the graphs of y = x and y = \(\frac{{{x}^{2}}}{2}\) is rotated around the line y = x. Find

  1. the centroid of the region and
  2. the volume of the solid of revolution.

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