EXAMPLE 4 The region R enclosed by the curves y = 2x and y = x² is rotated about the x-axis. Find the volume of the resulting solid. SOLUTION The curves y = 2x and y = x² intersect at the points (0. and (2.0 The region between them, the solid of rotation, and a y=2x cross section perpendicular to the x-axis are shown in the figures. A cross-section in the plane Px has the shape of a washer (an annular ring) with inner radius and an outer radius , so we find the cross-sectional area by subtracting the area of the inner circle from the area of the outer circle: A(x)=4x-(x²)² = m Therefore, we have v =