Below, we see a region bounded by two curves.

The region shaded in light blue is bounded on the left by the curve $x=\frac{1}{16}{y}^2($in dark red$),$ on the right by the curve $y=\frac{1}{4}x($in dark blue$).$

Part $1.$

Suppose that we wish to integrate with respect to $x$ to find the value of the shaded area. Fill in the blanks so that the resulting integral $($with respect to $x)$ will describe the area of the shaded region.

$=\{\begin{array}{c}\text{:}[256]\\ 0\end{array}$

Note: Set up the integral so that the lower limit of integration is less than the upper limit of integration.

Part $2.$

$=$

Note: Set up the integral so that the lower limit of integration is less than the upper limit of integration.

Part $3.$

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