Find the volume of the solid

Question

Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=1/x, y=0, x=1 and x=4 about the x-axis

Answer 1

Volume of typical disk = π(radius)²(thickness)

 

                                       = π(1/x)²dx

 

                                       = πx^-2dx

                                 _{4                                 4}

Volume of solid = ∫  πx^-2dx = π[-1/x]    = π[(-1/4)-(-1)] = 3π/4

                                 ^{1                                 1}