$\"\"$

The function is $\"\"$ .

Observe the graph :

When we rotate a thin horizantal strip as shown in the figure about the $\"\"$ axis, we get a disc with radius $\"\"$ .

The width of the disc is $\"\"$ .

The volume of the solid of revolution is $\"\"$ .

From the graph, $\"\"$ and $\"\"$ .

Substiute the values in $\"\"$ .

$\"\"$

Therefore, the integral that gives the volume of the solid formed by revolving the region about the $\"\"$ -axis is $\"\"$ .

$\"\"$

$\"\"$ .