A hemispherical plate with diameter $10$ ft is submerged vertically $2$ ft below the surface of the water. Express the hydrostatic force against one side of the plate as an integral and evaluate it$.($Round your answer to the nearest whole number. Recall that the weight density of water is $62\mathrm{.}5l\frac{b}{f}{t}^3.)$

$2$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}dy$~~ $$ lb