Let R be the shaded region bounded by the graph of $\displaystyle y=lnx$ and the line $\displaystyle y=x-2$.

Find the volume of the solid generated when R is rotated about the horizontal line y=-3.

Is this the correct integral for the volume?

$\displaystyle \pi \int^{0.15859434}_{3.1461932} [{(lnx)^2-(x-2)^2}]dx$