Hydrostatic Pressure (Hydrostatic Force)

Hello. I am actually an active member of a science forum, and have gotten help learning from its math members for a good three or four months, and am impossibly grateful to them for their time, however that help has recently seemed to drop off. I now find myself stuck in the application of integration to hydrostatic pressure. I apologize if it seems unethical of me to post a link to another website, but I have done a great deal of posting describing my problem in this science forum's math section. This is the link to my thread where 13 posts down I begin to describe where I have been stuck for two weeks.

(website removed by Demen)

I would be very grateful if I could get some help so I can understand what I am doing wrong. I will surely repay your effort by sharing my time here, on the MHF to help answer calculus questions of the fellow members.