Pressure exerted on the end of a pool

[JCL]

Homework Statement

Consider a
trough with triangular ends, as pictured below, where the tank is 10 feet long, the top is 5
feet wide, and the tank is 4 feet deep. Say that the trough is full to within 1 foot of the top with water
of weight density 62.4 pounds/ft^3. How much force does the water exert against one of the triangular
ends?

Homework Equations

F=pgxa The given picture has the axis rotated 90 degrees clockwise

The Attempt at a Solution

I took the integral from 0 to 3 of p * g * x * a dx
so I got integral of 0 to 3 of (62.4 lbs/ft^3)(g)(4-x)(10(5-1.25x) dx
which can be written as 624g integral (4-x)(5-1.25x) dx
is this set up correct?

 

[Merlin3189]

Pressure depends on ...?
So force is ρgha as you say. So where does the length of trough creep into your calculation?

I think it's your expression for a that is wrong, (10(5-1.25x) , as well as the missing bracket.

 

[haruspex]

integral from 0 to 3 of p * g * x * a dx
so I got integral of 0 to 3 of (62.4 lbs/ft^3)(g)(4-x)(10(5-1.25x) dx

How exactly are you defining x? The above is not consistent.