Final answer:
To express the hydrostatic force against one side of a plate as an integral, you can use the equation for hydrostatic pressure and multiply it by the area of the plate. The integral expression for the hydrostatic force against one side of the plate is F = ∫[πgh(x)] * A(x) dx.
Step-by-step explanation:
To express the hydrostatic force against one side of a plate as an integral, we can use the equation for hydrostatic pressure. The hydrostatic pressure is calculated using the formula P = πgh, where P is the pressure, π is the fluid density, g is the acceleration due to gravity, and h is the height of the fluid column. To calculate the hydrostatic force, we multiply the pressure by the area of the plate using the equation F = P * A. So, the integral expression for the hydrostatic force against one side of the plate can be written as:
F = ∫[πgh(x)] * A(x) dx