(Solution) - Let R be the region bounded by the curves y -(2025 Original AI-Free Solution)

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Let R be the region bounded by the curves y = 1 ? x2 and y = x6 ? x + 1. Estimate the following quantities.
(a) The -coordinates of the points of intersection of the curves
(b) The area of R
(c) The volume generated when R is rotated about the x-axis
(d) The volume generated when R is rotated about the y-axis