I got this problem wrong and I need help because I don't know what I did wrong.

My answer: 2666.67 lb

Correct answer: 2133.3 lb

Here's the question:

A trough is filled with water and its vertical ends have the shape of the parabolic region in the figure. Find the hydrostatic force on one end of the trough.

Here is my attempt:

When units are in feet, Force=δdA

Where δ=62.5 $\displaystyle lb/ft^3$

d= depth of the water

A= area

so I start of by finding the equation of the parabola by drawing axes on the picture.

By looking at the graph I can tell the equation will look something like

$\displaystyle y=Cx^2+0$ //where C is a constant

using points on graph I get

$\displaystyle 4=C(4)^2$

4=16C

C=$\displaystyle \frac{1}{4}$ or 0.25

I get $\displaystyle f(x)=0.25x^2$

Next what I did was find the area

$\displaystyle A= \int_{-4}^4 0.25x^2 dx$

I integrated and i got

$\displaystyle A=\frac{32}{3} ft^2$

Now that I have found A i can plug all into the Force formula

F=δdA

=(62.5 $\displaystyle lb/ft^3$)(4ft)($\displaystyle \frac{32}{3} ft^2$)

F≈2666.67 lb <-------------- ANSWER IS INCORRECT PLEASE HELP!

What did I do incorrectly?