Please show all steps and details of the work:

Use the shell method to find the volume of the solid of revolution generated by revolving the shaded region bounded by the graphs of

?(?)= ??^2+5 and?(?)= 3?+1 and the? axis about the? axis.

The graph is not drawn to scale. The graphs?and?intersect at(1,4). (see attached picture for reference)

(Express numbers in exact form. Use symbolic notation and fractions where needed.) Volume: ____________________________

Now, use either the disk/washer method to find the volume of the solid of revolution generated by revolving the shaded region bounded by the graphs of?(?)=??2+5and?(?)=3?+1and the?- axis about the?- axis. (same graph)

(Express numbers in exact form. Use symbolic notation and fractions where needed.) Volume: ____________________________

The graph is not drawn to scale. The graphs f and g intersect at (1, 4)