$\"\"$

\

The integral is $\"\"$ .

\

Rewrite the integral as:

\

$\"\"$ .

\

Find the value of $\"\"$ using Simpson $\"\"$ s rule.

\

In this case $\"\"$ .

\

Width $\"\"$ .

\

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

\

$\"\"$ .

\

$\"\"$ .

\

Find the function values.

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ and $\"\"$ values in $\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

Simpson $\"\"$ s rule :

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ $\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

Show that $\"\"$ :

\

Consider $\"\"$ and $\"\"$ .

\

$\"\"$ for all $\"\"$ .

\

The function $\"\"$ is an increasing function.

\

Therefore, $\"\"$ on $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

Find the value of $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ is less than $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ .