Please help me with this math question

Question

Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x = 1 is revolved around the line y = -1. 

Answer 1

Intersection of curves y = lnx and y = 1 give us equation lnx = 1, or x = e;

Becouse 1 ≤ x ≤ e, external radius R = 1 - (- 1) = 2 and inner radius of rotation r = lnx - (- 1) = lnx + 1;

so volume V = π∫₁^e[2² - (lnx + 1)²]dx = π∫₁^e(3 - ln²x - 2lnx)dx;

Sorry, but I can't make picture with this editor..

Answer 2