Curved surface FP2

http://filestore.aqa.org.uk/subjects/AQA-MFP2-W-QP-JUN11.PDF

Question 5.

I'm sitting on S = 2πy∫√(1 +x^2/(x^2+8))

And i'm struggling to get to what they want me to show.

Help pls

I'm very alarmed by the fact that you have the $y$ outside the integral sign... correct version:

$\displaystyle 2\pi \int_0^6 \sqrt{x^2 + 8} \sqrt{\frac{x^2 + 8 + x^2}{x^2 + 8}} \, \mathrm{d}x = 2\pi \int_0^6 \sqrt{2(x^2 + 4)} \, \mathrm{d}x$

i can never tell when we can just ignore the minus root, in this case y has two values............ this makes me sad.

It would have made no difference had you taken the negative root - you'd get a negative area from which (I hope) you'd take the absolute value of to get the positive answer anyway. But at A-Level, you're nearly always going to be taking the positive root without any justification.

In either case - y is inside the integral!