Calculus: Early Transcendentals, Chapter 6, 6.2, Section 6.2, Problem 6

You need to evaluate the volume of the solid obtained by the rotation of the region bounded by the curves y = ln x , y = 1, y = 2,x=0 about y axis, using washer method, such that:
V = int_a^b (f^2(x) - g^2(x))dx, f(x)>g(x)
You may evaluate the volume
V = pi*int_1^2 (e^y - 0^2)^2dy
V = pi*int_1^2 e^(2y)dy
V = (pi/2)*(e^(2y))|_1^2
V = (pi/2)*(e^(2*2) - e^(2*1))
V = (pi/2)*(e^4 - e^2)
Hence, evaluating the volume of the solid obtained by the rotation of the region bounded by the curves y = ln x , y = 1, y = 2,x=0 about y axis, yields V = pi*(e^4 - e^2)/2.