Having a bit of trouble with this one. Can anyone help me out?

Many thanks.

The given diagram (see attachment) shows the line [tex]y=2x[tex]. Find the volume generated when this line is rotated about the x-axis from to

Q.

Attempt:If , the height of the generated volume is also 3.

For , . Thus, the height of the volume generated is 6.

Volume:

Ans.:(From text book):