$\"\"$

\

The equation is $\"\"$ .

\

The base of the plate is $\"\"$ beneath the surface of the water.

\

$\"\"$

\

Observe the graph:

\

The height of the vertical plate is $\"\"$ .

\

The horizontal length of the vertical plate is $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Therefore, $\"\"$ .

\

The fluid force is $\"\"$ .

\

The limits are $\"\"$ to $\"\"$ .

\

The weight density of water is $\"\"$ .

\

Substitute $\"\"$ , $\"\"$ and $\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

Consider the integrand as function $\"\"$ .

\

Graph the function $\"\"$ .

\

$\"\"$ .

\

Observe the graph:

\

$\"\"$ .

\

$\"\"$ .

\

Therefore, $\"\"$ .

\

$\"\"$

\

$\"\"$ .