$\"\"$

\

(a)

\

The curves are $\"\"$ and $\"\"$ and the region is rotated about $\"\"$ .

\

Method of Cylinders :

\

The volume of the solid obtained by rotating about $\"\"$ -axis, the region of the curve $\"\"$ from $\"\"$ to $\"\"$ is

\

$\"\"$ .

\

Here rotation is about the line $\"\"$ .

\

Hence the radius is $\"\"$ .

\

Height is $\"\"$ .

\

Find the point of intersections.

\

Find the value of $\"\"$ for $\"\"$ and $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ and $\"\"$

\

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

\

Integral limits are $\"\"$ and $\"\"$ .

\

Set up the integral for the volume using above volume formula.

\

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

\

Find the volume obtained by rotating region about $\"\"$ , bounded by the curve $\"\"$ and $\"\"$ from $\"\"$ to $\"\"$ is $\"\"$

\

$\"\"$ .

\

$\"\"$

\

(b)

\

Use calculator to find $\"\"$ .

\

Therefore the result is $\"\"$ .

\

$\"\"$

\

(a) $\"\"$ .

\

(b) $\"\"$ .