Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=1/x, y=0, x=1 and x=4

Question

about the line y=−1

Answer 1

v = ∫[1,4] π(R^2-r^2) dx
where R=(1/x + 1) and r=1
v = ∫[1,4] π((1/x + 1)^2-1^2) dx = π(3/4 + ln16)

check, using shells of thickness dy:
v = ∫[0,1/4] 2πrh dy
where r=y+1 and h=3
+ ∫[1/4,1] 2πrh dy
where r=y+1 and h=(1/y - 1)

Crank it out, and you get the same answer.