Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis y = 3x^2, y = 18x − 6x^2

Answer24πexplanationthe region in question is graphed out in the attachment. the method of cylindrical shells revolving around the y-axis:     region goes from x = 0 to x = 2 so    a = 0 and b = 2the radius is the x-coordinate (in the region 0  ≤ x  ≤ 2)    radius = xthe height is the top function minus the bottom function:     height =  (18x - 6x²) - (3x²)    height = 18 - 9x²the volume is therefore   

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