Final answer:
To find the volume of the solid obtained by rotating the region bounded by the curves y = x and y = x about the line x = 2, 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 = x and y = x about the line x = 2, we can use the method of cylindrical shells.
The volume of each shell is given by 2πrΔx, where r is the distance from the line x = 2 to the curve y = x, and Δx is the width of the shell.
Since y = x represents a line passing through the origin, the distance from the line x = 2 to the curve y = x is 2 units. So, the volume of each shell is 2π(2)(Δx) = 4πΔx.
To find the total volume, we need to integrate 4πΔx over the interval [0,1]. The integral will give us the volume of the solid.