Find the volume of the solid formed by revolving the region bounded by the graphs of y = x^3, x = 2, and y = 1 about the y-axis.

Question

Question options:

1)
2)
3)
4)	None of these

Answer 1

WE use shell method. Volume V = ∫₁²2πx(x³ - 1)dx = 2π(x⁵/5 - x²/2)₁² = 2π((2⁵/5 - 2²/2) - (1⁵/5 - 1^2/2)) =

^47π/5.

^{Answer is 3), V = 47π/5}

^{Sorry I can't do picture uzing this editor.}