4.
\includegraphics[max width=\textwidth, alt={}, center]{ef0c9a48-9d23-48ed-89b8-2e116114d7ed-07_527_718_191_651} The diagram shows the curves \(y = \mathrm { e } ^ { 3 x }\) and \(y = ( 2 x - 1 ) ^ { 4 }\). The shaded region is bounded by the two curves and the line \(x = \frac { 1 } { 2 }\). The shaded region is rotated completely about the \(x\)-axis. Find the exact volume of the solid produced.