34. (B)
Use disks; then ΔV = πR^2 H = π(ln y)^2 Δy. Note that the limits of the definite integral are 1
and 2. Evaluate the integral
Alternatively, use shells*; then ΔV = 2πRHT = 2πx(2 − ex) Δx. Here, the upper limit of
integration is the value of x for which ex = 2, namely, ln 2. Now evaluate
* No question requiring the use of the shells method will appear on the AP exam.