Let f be the function defined by f(x) = ln(x) for 0 < x 1. R is the region between the graph of f and the x-axis.

1.This question does not permit the use of a calculator.

Determine whether the solid generated by revolving region R about the y-axis has a finite volume. If so, find the volume. If not, explain why.

2 Find the volume of the solid whose base is the region bounded by f(x), g(x) and the x-axis on the interval [0, 1], and whose cross-sections perpendicular to the y-axis are squares. g(x)=x^2

Your work must show the integral, but you may use your calculator to evaluate it. Give 3 decimal places for your answer.