Let f be the function defined by f(x) = ?ln(x) for 0

1. This question does not permit the use of a calculator. Determine whether region R has a finite area. If so, find the area. If not, explain why.

2. 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.

3. The formula for the arc length from a to b of a differentiable function is

Find the length of the curve f(x) from x = 0.5 to x = 1. Your work must show the integral, but you may use your calculator to evaluate it. Give 3 decimal places in your answer.

4. g(x) = x ² . Find the area bounded by f(x), g(x) and the x-axis in the interval [0.5, 1]. Your work must show the integral, but you may use your calculator to evaluate it. Give 3 decimal places in your final answer.

L = b a 1 + [f'(x)] dx