Final answer:
To find the volume of the solid, use the method of cylindrical shells by integrating the volumes of vertical slices of the region.
Step-by-step explanation:
To find the volume of the solid obtained by rotating the region bounded by the curve f(x) = 2eˣ - 7, the x-axis, the y-axis, and the line x = 1 around the y-axis, we can use the method of cylindrical shells. Cylindrical shells are formed by taking vertical slices of the region and rotating them around the y-axis. The volume of each shell can be approximated as the product of its height, circumference, and thickness. By integrating these volumes over the range of y-values, we can find the total volume of the solid.