Below, we see a region bounded by two curves and the $x-$axis.

The region shaded in light blue is bounded on the left by the curve $y=2x($in dark blue$),$ on the right by the curve $y=\frac{1}{4}{x}^2($in dark red$),$ and above by the line $y=2($in dark green$).$

Part $1.$

Part $2.$

$=$

Part $3.$

Finally, after evaluating the integrals above, we find that the area of the shaded region equals $$