Hydrostatic force with a gate?

THis is my last question, I promise!! Here is the problem: a vertical dam has a semicircular gate. Find the hydrostatic force against the gate. The picture is a square with a semicircle at the bottom in the middle. The diameter of that semicircle is 4 m. The height of the square dam thing is 12 m and the water level is 2m down. So I thought you integrate from 2 to 12, and then I don't know what to do next, I should be learning from these, but they're getting really hard! Would you find the area of the semicircle? and then the pressure against the gate. There's water and everything is in meters, so I think you use 1000 *9.8 times the depth for the pressure, but the depth varies on the gate. Help! THanks!! (Thinking)