A cable hangs between two poles of equal height and $40$ feet apart.

At a point on the ground directly under the cable and $x$ feet from the point on the ground halfway between the poles the height of the cable in feet is

$h(x)=10+(0\mathrm{.}1)(x^{1\mathrm{.}5})$

The cable weighs $17\mathrm{.}1$ pounds per linear foot.

Find the weight of the cable.