Answer
$$V \approx 3.2332$$
Work Step by Step
$$\eqalign{
& y = \ln x,{\text{ }}y = 0,{\text{ }}x = 1,{\text{ }}x = 3 \cr
& V = \pi \int_a^b {{{\left[ {R\left( x \right)} \right]}^2}} dx \cr
& {\text{Let }}R\left( x \right) = \ln x \cr
& {\text{So}},{\text{ the volume of the solid of revolution is}} \cr
& V = \pi \int_1^3 {{{\left( {\ln x} \right)}^2}} dx \cr
& V = \pi \int_1^3 {{{\ln }^2}x} dx \cr
& {\text{Integrating by using the integration capability of a scientific }} \cr
& {\text{calculator, we obtain}} \cr
& V \approx \pi \left( {1.02917} \right) \cr
& V \approx 3.2332 \cr} $$
