A vertical plate is submerged in water and has the shape as seen in the picture. Assume that the measurements shown in the picture have U.S. Customary units. Using the fact that the weight of water is $62.5\; lb/ft^3$, calculate the hydrostatic force (in lbs) against the plate.

(Hint: First set up a Riemann sum that approximates the hydrostatic force, which can then be used to obtain an integral that represents the force. Your answer may be in terms of $a$, $b$, and $h$.)



Hydrostatic force = lbs