A vertical dam has a semicircular gate as shown in the figure. The total depth $d$ of the figure is $38$ m $,$ the height $h$ of air above the water level is $6$ m $,$ and the width w of the gate is $10$ m $.$

Set up an integral that can be used to find the hydrostatic force $($in N$)$ against the gate. $($Use $9\mathrm{.}8\frac{m}{s^2}$ for the acceleration due to gravity. Assume that the weight density of this water is $1,000k\frac{g}{m^3}.)$

Find the hydrostatic force $($in N$)$ against the gate. $($Round your answer to the nearest whole number.$)$

N