x(x-y) wrote:

Not to sound cocky, but I rarely get stuck on homework questions but this one (from the "OCR Advanced Mathematics Core 3 and 4" book, just in-case you're wondering) has got me scratching my head:

"The region enclosed by both axes, the line x = 2 and the curve

$ \displaystyle y=\frac{1}{8}x^{2} + 2$

is rotated about the y-axis to form a solid. Find the volume of this solid".

You were on the right track but you got the sign and the integral wrong.

$ \displaystyle Vol = \pi \times 2^2 \times \frac {5}{2} - \int_2^{\frac{5}{2}} 8 \pi (y-2) dy = 9 \pi$