$22.$ The end plates $($isosceles triangles$)$ of the trough shown to the right were designed to withstand a fluid force of $5400$ lb $.$ Assuming the density of water is $62\mathrm{.}4l\frac{b}{f}{t}^3,$ how many cubic feet can the trough hold without exceeding this limitation$?$ What is the value of $h,$ the depth of water that exerts a fluid force of $5400$ lb $?$

What is the integral that gives the fluid force exerted on the end of the trough when filled with water to a depth of $h?$

Please answer all three parts