$\"\"$

The parametric equations of the curve are $\"\"$ and $\"\"$ .

The interval is $\"\"$ and $\"\"$ .

Length of the curve with parametric equations $\"\"$ and $\"\"$ , $\"\"$ is $\"\"$ .

Consider $\"\"$ .

Diffrentiate with respective to $\"\"$ .

$\"\"$

Consider $\"\"$ .

Diffrentiate with respective to $\"\"$ .

$\"\"$ .

From the double angle formula : $\"\"$ .

$\"\"$ .

$\"\"$

Find the length of the curve.

Theorem :

If a curve is described by the parametric equations $\"\"$ and $\"\"$ , $\"\"$

then the length of the arc is $\"\"$ .

Where $\"\"$ .

Substitute $\"\"$ , $\"\"$ and limits of $\"\"$ in formula.

$\"\"$

Find the width of the intervals :

Simpsons rule:

Let $\"\"$ be continuous on $\"\"$ let $\"image\"$ be an even integer,

The Simpsons Rule for approximating $\"\"$ is given by

$\"\"$ , where $\"\"$ and $\"\"$ .

Calculate the value of $\"\"$ .

Where $\"\"$ and $\"\"$ .

$\"\"$

Here $\"\"$ .

Calculate $\"\"$ at the interval boundaries.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Write down the simpsons rule for $\"\"$ terms and substiute the values in the table.

$\"\"$ .

$\"\"$

Arc length of the curve is $\"\"$ .