Let f be the function defined by f(x) = ?ln(x) for 0 1. This question does not
Question:
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.