Hydrostatic pressure and force is an important application of integrals, also used in Physics. In this topic we deal with pressure and force exerted by fluids on submerged plates.
When rectangular plate is submerged horizontally then force acting on it, is constant but when it is submerged vertically in water then pressure acting on it, is not constant throughout, so force acting on it must be calculated using slicing which leads to integral. Here you can find some examples on this topic. https://celestialtutors.com/subtopic/fluid-pressure-and-force/