4.
\includegraphics[max width=\textwidth, alt={}, center]{11e1fe10-7d93-4a49-9151-83b40391a329-07_520_714_196_653} 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.