$\"\"$

\

Region is bounded by the graphs $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

\

Find the surface area of the solid generated by revolving the region about $\"\"$ axis.

\

Definition of the surface area:

\

If the curve $\"\"$ , $\"\"$ , then the surface area of the curve is defined as $\"\"$ .

\

Consider $\"\"$ .

\

Differentiate on each side with respect to $\"\"$ .

\

$\"\"$ .

\

And here $\"\"$ .

\

Substitute corresponding values in the formula.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Find the integral using trigonometric substitution.

\

$\"\"$ .

\

$\"\"$

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Formula: $\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

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

\

$\"\"$

\

If $\"\"$ then $\"\"$ .

\

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

\

Consider $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Surface area of the solid is $\"\"$ sq-units.

\

$\"\"$

\

Surface area of the solid is $\"\"$ sq-units.