This is a very general question about the type of problems involved in this topic.
Basically: how do I know when the problem I am working is a plug-in problem, or a problem that requires integral calculus? I've seen examples done through both methods.
For instance, this was a plug-in problem:
"A rectangular pool 20 m long, 15 m wide, and 4 m deep is filled with a fluid of density 1020 kg/m^3 to a depth of 3 meters. Find the hydrostatic force on the bottom of the pool. "
To answer this, I would simply use the formula F= rho*g*d*A
But this problem requires calculus:
"A dam with the shape of a trapezoid has a height of 20 m and a width of 50 m at the top and 30 m at the bottom. Find the force on the dam due to hydrostatic pressure if the water level is 4 m from the top of the dam"
Is that because the first problem asks for the specific force on a specific portion of the dam where as the second problem asks for the change in the force as you move downward from the top of the water level?