$\"\"$

\

The equation of the ellipse is $\"\"$ .

\

Find the arc length of the ellipse.

\

The arclength of the ellipse is $\"\"$ .

\

Consider $\"\"$ .

\

$\"\"$

\

Here $\"\"$ and $\"\"$ .

\

The eccencrtity is $\"\"$ .

\

Substitute the corresponding values.

\

$\"\"$ .

\

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

\

Graph the function $\"\"$ on interval $\"\"$ .

\

$\"\"$

\

Observe the graph:

\

$\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Therefore, the arclength of the ellipse is $\"\"$ .

\

$\"\"$

\

The arclength of the ellipse is $\"\"$ .