Find the volume of the solid revolved around y=x^3, y=1, x=2 about the line x=2

Answer 1

Integration limits: x³ = 1; x = 1 and x = 2. Byn shell method volume V = 2π∫₁²(2 - x)(x³ - 1)dx =

2π∫₁²(2x³ - x⁴ + x - 2)dx = 2π(x⁴/2 - x⁵/5 + x²/2 - 2x)₁² = 2π[(8 - 32/5 + 2 - 4) - (1/2 - 1/5 + ,1/2 - 2)] = 8π/5