calculus 2

Question

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis.

 

y = 1/x
y = 0
x = 3
x = 9

Answer 1

Use the disk method.  A typical disk perpendicular to the x-axis has volume π(1/x)²Δx

 

Volume = ∫_{(from 3 to 9)} π(1/x) ²dx = π(-1/x)_{(from 3 to 9)}

 

                                        = -(π)[1/9-1/3] = 2π/9