Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. y = x3, y = 8, x = 0; about x = 9

Answer:200π cubic units.Step-by-step explanation:Use the general method of integrating the area of the surface  generated by an arbitrary cross section of the region  taken parallel to the axis of revolution.Here the axis  x = 9 is parallel to the y-axis.The height of  one cylindrical shell = 8 - x^3. The radius = 9 - x.                                                2The volume generated =  2π∫   (8 - x^3) (9 - x) dx                                                0= 2π ∫ ( 72 - 8x - 9x^3 + x^4) dx              2=      2 π [    72x - 4x^2 - 9x^4/4 + x^5 / 4  ]             0= 2 π  ( 144 - 16  - 144/4 + 32/4)= 2 π * 100= 200π.