A cable hangs between two poles of equal height and $36$ 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
$$h(x)=10 +(0.2)( x^{1.5}) .$$ The cable weighs 11.8 pounds per linear foot.
Find the weight of the cable.