Using disk washers, find the volume of the solid obtained by rotating the region bounded by the curves y=sec(x), y=1, x=−1, and x=1 about the x-axis.

General integral for volume using washer method:


First determine limits along x-axis.
region is bounded by x=1 and x=-1, so the limits are also -1 and 1.

Next determine R(x) and r(x)
R is the long radius, which is distance from x-axis to upper bound.
The upper bound of region is y = sec(x).
R = sec(x)

r is the short radius, which is distance from x-axis to lower bound.
The lower bound is y = 1.
r = 1

Sub into integral:


Integrate


Evaluate