I don't think that you have enough bounds on your region...
The finite region bounded by the curve , the y-axis, and the line , is rotated through 360 degrees about the x-axis. Show that the volume of the solid formed is .
Volume = , with limits
This becomes: Volume = , with limits
(We can take pi outside the integral and multiply the result by it later).
Integrating term by term:
So my answer is:
So I don't know how they've reached the answer given.
Also, I found that if you multiply out the answer given, you get . My answer is equivalent to , so I just can't see how they got the second part.
Anyone else have any ideas?