The ProblemThe 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 .

AttemptVolume = , 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:

.

Substituting :

Substituting :

Subtracting:

.

So my answer is:

.

So I don't know how they've reached the answer given.

Any hints?