The curve is  ,the line is , and the region is rotated about .

(a)

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 .

Integral limits are and .

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

Find the volume of the solid obtained by rotating region about , bounded by the curve and from to is

.

(b)

Use calculator to find .

Therefore the result is .

(a) .

(b) .