SCalkET$98\mathrm{.}3\mathrm{.}012$ EP$.$

A vertical dam has a semicircular gate as shown in the figure. The total depth $d$ of the figure is $12$ m $,$ the height $h$ of air above the water level is $2$ m $,$ and the width $w$ of the gate is $2$ 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 $1,000k\frac{g}{m^3}.)$

${\displaystyle \underset{0}{\overset{\phantom{}}{}}},x^{(1,000)(9\mathrm{.}8)}(x)dx$

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

$N$

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