1.Find the centroid of the region bounded by the curve 𝑦 = 𝑥3 and 𝑦 = 4𝑥 in the first quadrant.
2. Find the centroid of the solid of revolution generated by revolving the region bounded by 𝑦 = 4𝑥 − 𝑥2 and the x-axis about the y-axis.
we are interested in the point in the first quadrant, the transition point is
where v = volume
finally we find the the centroid: