Final answer:
To 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, we can use the method of cylindrical shells.
Step-by-step explanation:
To 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, we can use the method of cylindrical shells.
The volume of the solid is given by the integral of the shell method formula V = 2π*∫(y*f(x))*dx, where y is the height of the shell at a given x-value and f(x) is the distance from x to the axis of rotation.
By substituting y=sec(x) and f(x)=x into the formula and evaluating the integral from -1 to 1, we can find the volume of the solid.