y=x^3 y=0 x=2 about y=8

Answer 1

Using the disk method, the volume of a typical vertical cross section is π(8 - x³)²dx.

Volume of solid = ∫_{(0 to 2)}[π(8 - x³)²dx

= π∫_{(0 to 2)}[64 - 16x³ + x⁶]dx

= π[64x - 4x⁴ + (1/7)x⁷]_{(0 to 2)}

= π(128 - 64 + 128/7) = 320π/7