Final answer:
The volume of the solid can be found using the method of cylindrical shells.
Step-by-step explanation:
To find the volume V of the solid obtained by rotating the region bounded by the curves y = 2 sec(x), y = 4, -3 ≤ x ≤ 3 about the line y = 2, we can use the method of cylindrical shells. This involves integrating the circumference of each shell multiplied by its height.
The radius of each shell is given by the distance between the line of rotation (y = 2) and the curve y = 2 sec(x). We can calculate this distance by subtracting the y-coordinate of the line of rotation from the y-coordinate of the curve.
The height of each shell is given by the difference between the straight line segment y = 4 and the curve y = 2 sec(x).