$\"\"$

\

The circumference of an ellipse is $\"\"$ , $\"\"$ .

\

Consider $\"\"$ .

\

In this case $\"\"$ .

\

Width $\"\"$ .

\

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

\

$\"\"$ .

\

Find the function values.

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

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

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

Simpsons rule :

\

$\"\"$ . $\"\"$

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$ .

\

The circumference of an ellipse is $\"\"$ units.

\

$\"\"$

\

The circumference of an ellipse is $\"\"$ units.