find the volume of solid of revolution generated when the region bounded by y=1-3/x,x-axis and line x=1?

Question

it revolve in x-axis

Answer 1

First find the x intercept of y = 1 - 3/x.
1 - 3/x = 0
1 = 3/x
x = 3

Integrate from x = 1 to x = 3.

Use the disk method.

∫πy²dx = π∫(1 - 3/x)²dx = π∫(1 - 6/x + 9/x²)dx

= π(x - 6lnx - 9/x) | [Evaluated from 1 to 3]

= π(3 - 6ln3 - 9/3) - π(1 - 6ln1 - 9/1)

= π(3 - 6ln3 - 3) - π(1 - 0 - 9)

= -6πln3 + 8π = 2π(4 - 3ln3) ≈ 4.4243875

Answer 2

If im not wrong , you are a year 2 JC student in Singapore rite?