Hi there!!!
First of all, It's been a long time since I read a Calculus book, thats mainly the reason I'm stuck here...
That being said, on to the problem:
Lets start by assuming that dF = P(z)*ds (as vectors, dF and ds)
So, if we integrate over the whole surface, we get the result that |F| = P[g]*A
with P[g] pressure at center of gravity and A area of the surface (plane for now)
BUT, thats making an analysis which I don't really like. I want to be able to solve the vectorial equation so I get the force in each axis right away and not getting the modulus of the Force and having to separate it knowing that it is applied perpendicularly to the surface.
So, how can I integrate each equation?
dF[x] = P(z) * ds[x], etc
Thank you
PS: Sorry, I'm really bad at explaining this stuff in english