6. [6 pts] Consider the region bounded by the curves y = ln x, y = 2, and x = 1 shaded in the figure below.
a) (3 pts) Write down a definite integral for the area of the shaded region. Do NOT evaluate the resulting integral.
b) (3 pts) Write down a definite integral for the volume of the solid generated when the shaded region is revolved about the y-axis. Do NOT evaluate the resulting integral.