Why is There a - Sign in an Integral?

[foo9008]

Homework Statement

why there is - sign in front of integral of (z2-z1)dA , is it a mistake ?

Homework Equations

The Attempt at a Solution

 

[Megaquark]

In your picture, they define the height of the volume element (a positive number) as z1-z2. This means that z1 must be the larger number. I'm guessing that they must be thinking of z=0 as the surface of the fluid, making z1 and z2 negative numbers...so they have the negative sign out front to make the force act in the positive z direction. Just a guess anyway.