$\"\"$

\

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 $\"\"$ .

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

\

$\"\"$

\

$\"\"$ .

\

Therefore, $\"\"$ .

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The fluid force is $\"\"$ .

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

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

\

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

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$\"\"$ .

\

$\"\"$

\

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

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Graph:

\

Graph the function $\"\"$ :

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$\"\"$ .

\

Observe the graph:

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$\"\"$ .

\

$\"\"$ .

\

Therefore, $\"\"$ .

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$\"\"$

\

$\"\"$ .