Use either the shell method or the disk/washer method to find the volume of the solid of revolution generated by revolving the shaded region bounded by the graphs of f(x) = −x2 + 21 and g ( x ) = 8x + 1 and the y -axis about the x -axis. The graph is not drawn to scale. The graphs f and g intersect at (2,17). (Express numbers in exact form. Use symbolic notation and fractions where needed.) volume:
![Consider a region R bounded by the functions f(x) = x2 + 1 and g(x) = x over the interval [0, 2]. (a) Draw an accurate graph of the region R. (b) Find the area of the region. (c) A solid of revolution is obtained by revolving a plane region bounded by a curve f(x), x ∈ [a, b], about x-axis. The volume of such solid is as V = π∫a b [f(x)]2 dx. Calculate the volume of the solid generated by the region R revolving about the x-axis.](https://www.doubtrix.com/uploads/editor/1782620418zjZNPxKVjz.png)
